Jingjing Dong, Xiaofeng Ma, Lan He, Xin Huang, Jianping Zhou
This paper investigates the issue of energy-to-peak control for continuous-time switched systems. A generalized switching signal, known as persistent dwell-time switching, is considered. Two different strategies for state-feedback controller design are proposed, using distinct Lyapunov functions and a few decoupling techniques. The critical distinction between these two strategies lies in their temporal characteristics: one is time-independent, while the other is quasi-time-dependent. Compared to the former, the latter has the potential to be less conservative. The validity of the proposed design strategies is demonstrated through an example.
{"title":"Energy-to-peak control for switched systems with PDT switching","authors":"Jingjing Dong, Xiaofeng Ma, Lan He, Xin Huang, Jianping Zhou","doi":"10.3934/era.2023268","DOIUrl":"https://doi.org/10.3934/era.2023268","url":null,"abstract":"This paper investigates the issue of energy-to-peak control for continuous-time switched systems. A generalized switching signal, known as persistent dwell-time switching, is considered. Two different strategies for state-feedback controller design are proposed, using distinct Lyapunov functions and a few decoupling techniques. The critical distinction between these two strategies lies in their temporal characteristics: one is time-independent, while the other is quasi-time-dependent. Compared to the former, the latter has the potential to be less conservative. The validity of the proposed design strategies is demonstrated through an example.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70247398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ontology serves as a central technique in the semantic web to elucidate domain knowledge. The challenge of dealing with the heterogeneity introduced by diverse domain ontologies necessitates ontology matching, a process designed to identify semantically interconnected entities within these ontologies. This task is inherently complex due to the broad, diverse entities and the rich semantics inherent in vocabularies. To tackle this challenge, we bring forth a new interactive ontology matching method with local and global similarity deviations (IOM-LGSD) for ontology matching, which consists of three novel components. First, a local and global similarity deviation (LGSD) metrics are presented to measure the consistency of similarity measures (SMs) and single out the less consistent SMs for user validation. Second, we present a genetic algorithm (GA) based SM selector to evolve the SM subsets. Lastly, a problem-specific induced ordered weighting aggregating (IOWA) operator based SM aggregator is proposed to assess the quality of selected SMs. The experiment evaluates IOM-LGSD with the ontology alignment evaluation initiative (OAEI) Benchmark and three real-world sensor ontologies. The evaluation underscores the effectiveness of IOM-LGSD in efficiently identifying high-quality ontology alignments, which consistently outperforms comparative methods in terms of effectiveness and efficiency.
{"title":"Interactive complex ontology matching with local and global similarity deviations","authors":"Xingsi Xue, Miao Ye","doi":"10.3934/era.2023291","DOIUrl":"https://doi.org/10.3934/era.2023291","url":null,"abstract":"Ontology serves as a central technique in the semantic web to elucidate domain knowledge. The challenge of dealing with the heterogeneity introduced by diverse domain ontologies necessitates ontology matching, a process designed to identify semantically interconnected entities within these ontologies. This task is inherently complex due to the broad, diverse entities and the rich semantics inherent in vocabularies. To tackle this challenge, we bring forth a new interactive ontology matching method with local and global similarity deviations (IOM-LGSD) for ontology matching, which consists of three novel components. First, a local and global similarity deviation (LGSD) metrics are presented to measure the consistency of similarity measures (SMs) and single out the less consistent SMs for user validation. Second, we present a genetic algorithm (GA) based SM selector to evolve the SM subsets. Lastly, a problem-specific induced ordered weighting aggregating (IOWA) operator based SM aggregator is proposed to assess the quality of selected SMs. The experiment evaluates IOM-LGSD with the ontology alignment evaluation initiative (OAEI) Benchmark and three real-world sensor ontologies. The evaluation underscores the effectiveness of IOM-LGSD in efficiently identifying high-quality ontology alignments, which consistently outperforms comparative methods in terms of effectiveness and efficiency.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70247657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jun Guo, Yanchao Shi, Weihua Luo, Yanzhao Cheng, Shengye Wang
The issues of exponential projective synchronization and adaptive exponential projective synchronization are analyzed for quaternion-valued memristor-based neural networks (QVMNNs) with time delays. Different from the results of existing decomposition techniques, a direct analytical approach is used to discuss the projection synchronization problem. First, in the framework of measurable selection and differential inclusion, the QVMNNs is transformed into a system with parametric uncertainty. Next, the sign function related to quaternion is introduced. Different proper control schemes are designed and several criteria for ascertaining exponential projective synchronization and adaptive exponential projective synchronization are derived based on Lyapunov theory and the properties of sign function. Furthermore, several corollaries about global projective synchronization are proposed. Finally, the reliability and validity of our results are substantiated by two numerical examples and its corresponding simulation.
{"title":"Exponential projective synchronization analysis for quaternion-valued memristor-based neural networks with time delays","authors":"Jun Guo, Yanchao Shi, Weihua Luo, Yanzhao Cheng, Shengye Wang","doi":"10.3934/era.2023285","DOIUrl":"https://doi.org/10.3934/era.2023285","url":null,"abstract":"The issues of exponential projective synchronization and adaptive exponential projective synchronization are analyzed for quaternion-valued memristor-based neural networks (QVMNNs) with time delays. Different from the results of existing decomposition techniques, a direct analytical approach is used to discuss the projection synchronization problem. First, in the framework of measurable selection and differential inclusion, the QVMNNs is transformed into a system with parametric uncertainty. Next, the sign function related to quaternion is introduced. Different proper control schemes are designed and several criteria for ascertaining exponential projective synchronization and adaptive exponential projective synchronization are derived based on Lyapunov theory and the properties of sign function. Furthermore, several corollaries about global projective synchronization are proposed. Finally, the reliability and validity of our results are substantiated by two numerical examples and its corresponding simulation.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70247876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In order to effectively mitigate the deterioration of pavement and roadbed, the need for extensive repairs and costly reconstruction ought to be minimized. Hence, this study introduces a novel approach towards long-term preservation of asphalt pavement, which conducts in-depth research on pavement maintenance decision-making using the decision tree method. The selection of appropriate decision-making indicators is based on their respective significance and the actual maintenance requirements, from which a comprehensive decision model for asphalt pavement maintenance is developed. By employing the Analytic Hierarchy Process (AHP) and a network-level optimization decision-making approach, this study investigates the allocation of maintenance decisions, structural preservation, optimal combinations of maintenance strategies, and fund allocation schemes. The result is the development of a project-level and network-level structural preservation decision optimization method. Furthermore, a decision-making module is designed to accompany this method, facilitating the visualization of comprehensive data and decision-making plans. This module enhances the effectiveness and efficiency of the decision-making process by providing a user-friendly interface and a clear presentation of data-driven insights and decision outcomes. The case study clearly proved the applicability and rationality of the long-term preservation strategy of structures based on intelligent decision-making, which laid the foundation for the sustainable development of pavement maintenance and development.
{"title":"Analysis of long-term maintenance decision for asphalt pavement based on analytic hierarchy process and network level optimization decision","authors":"Jiuda Huang, Chao Han, Wuju Wei, Chengjun Zhao","doi":"10.3934/era.2023299","DOIUrl":"https://doi.org/10.3934/era.2023299","url":null,"abstract":"In order to effectively mitigate the deterioration of pavement and roadbed, the need for extensive repairs and costly reconstruction ought to be minimized. Hence, this study introduces a novel approach towards long-term preservation of asphalt pavement, which conducts in-depth research on pavement maintenance decision-making using the decision tree method. The selection of appropriate decision-making indicators is based on their respective significance and the actual maintenance requirements, from which a comprehensive decision model for asphalt pavement maintenance is developed. By employing the Analytic Hierarchy Process (AHP) and a network-level optimization decision-making approach, this study investigates the allocation of maintenance decisions, structural preservation, optimal combinations of maintenance strategies, and fund allocation schemes. The result is the development of a project-level and network-level structural preservation decision optimization method. Furthermore, a decision-making module is designed to accompany this method, facilitating the visualization of comprehensive data and decision-making plans. This module enhances the effectiveness and efficiency of the decision-making process by providing a user-friendly interface and a clear presentation of data-driven insights and decision outcomes. The case study clearly proved the applicability and rationality of the long-term preservation strategy of structures based on intelligent decision-making, which laid the foundation for the sustainable development of pavement maintenance and development.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70247894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A three-dimensional dynamic heat transfer mathematical model of the process when cored wire feed in molten iron is established based on finite volume method (FVM). The calculation area is meshed with triangles and quadrilaterals to determine nodes and control volumes, and implicit time integration method is used to ensure the stability of calculating process. For exposing the dynamic heat transfer behavior, the variation of temperature field and explosion characteristics of cored wires are studied. In addition, the melt loss rate of the top end of cored wire and the correlation among melt explosion depth, molten iron temperature and feeding speed of cored wires are theoretically calculated. More importantly, the influence of different structures of cored wires on the absorption rate of magnesium are considered. The calculation results are in good agreement with the experimental data, which indicate that the existing theoretical model has good validity and can provide theoretical guidance for spheroidization process in molten iron.
{"title":"Mathematical modeling and simulation analysis of different structured cored wire feeding spheroidization by finite volume method","authors":"Huiming Wang, Yimin Shi, Xingshi He, Wenzhi Zhao","doi":"10.3934/era.2023202","DOIUrl":"https://doi.org/10.3934/era.2023202","url":null,"abstract":"A three-dimensional dynamic heat transfer mathematical model of the process when cored wire feed in molten iron is established based on finite volume method (FVM). The calculation area is meshed with triangles and quadrilaterals to determine nodes and control volumes, and implicit time integration method is used to ensure the stability of calculating process. For exposing the dynamic heat transfer behavior, the variation of temperature field and explosion characteristics of cored wires are studied. In addition, the melt loss rate of the top end of cored wire and the correlation among melt explosion depth, molten iron temperature and feeding speed of cored wires are theoretically calculated. More importantly, the influence of different structures of cored wires on the absorption rate of magnesium are considered. The calculation results are in good agreement with the experimental data, which indicate that the existing theoretical model has good validity and can provide theoretical guidance for spheroidization process in molten iron.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70246286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper presents a two-stage method combining data envelopment analysis (DEA) and a Tobit model to analyze the comprehensive operating efficiency of 28 airports in China in 2016. At the first stage, the DEA-BCC (Banker-Charnes-Cooper) model was employed to obtain the comprehensive operating efficiency of the combination of flight departure punctuality, non-cancellations, landing bridge rates from the perspective of airport infrastructure, surrounding airspace, route layouts, flight volume and weather. At the second stage, a Tobit model was used to analyze the influence of nine input variables from four aspects on obtained comprehensive operating efficiency, ultimately providing a clear and straightforward basis for formulating and testing policies. The comprehensive operating efficiency with this combination was further compared with each of the three efficiencies respectively. The important findings included the following: (1) The comprehensive operation efficiencies of most airports were greater than the individual efficiency; (2) These four types of operation efficiencies for most airports did not achieved DEA validity (100% efficiency), except for six airports (i.e., Haikou, Dalian, Jinan, Fuzhou, Nanning and Lanzhou); (3) These factors affecting each of the four types of operation efficiencies were different in that the number of terminals, duration of impact and average daily inbound and outbound flights had a negative impact on airport operational efficiency, while the average number of overnight aircraft per day and peak hour sorties had positive effects.
{"title":"Comprehensive operating efficiency measurement of 28 Chinese airports using a two-stage DEA-Tobit method","authors":"Ming Wei, Shao-yun Zhang, Bo Sun","doi":"10.3934/era.2023078","DOIUrl":"https://doi.org/10.3934/era.2023078","url":null,"abstract":"This paper presents a two-stage method combining data envelopment analysis (DEA) and a Tobit model to analyze the comprehensive operating efficiency of 28 airports in China in 2016. At the first stage, the DEA-BCC (Banker-Charnes-Cooper) model was employed to obtain the comprehensive operating efficiency of the combination of flight departure punctuality, non-cancellations, landing bridge rates from the perspective of airport infrastructure, surrounding airspace, route layouts, flight volume and weather. At the second stage, a Tobit model was used to analyze the influence of nine input variables from four aspects on obtained comprehensive operating efficiency, ultimately providing a clear and straightforward basis for formulating and testing policies. The comprehensive operating efficiency with this combination was further compared with each of the three efficiencies respectively. The important findings included the following: (1) The comprehensive operation efficiencies of most airports were greater than the individual efficiency; (2) These four types of operation efficiencies for most airports did not achieved DEA validity (100% efficiency), except for six airports (i.e., Haikou, Dalian, Jinan, Fuzhou, Nanning and Lanzhou); (3) These factors affecting each of the four types of operation efficiencies were different in that the number of terminals, duration of impact and average daily inbound and outbound flights had a negative impact on airport operational efficiency, while the average number of overnight aircraft per day and peak hour sorties had positive effects.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70244212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
With the development of remote sensing technology, the resolution of remote sensing images is improving, and the presentation of geomorphic information is becoming more and more abundant, the difficulty of identifying and extracting edge information is also increasing. This paper demonstrates an algorithm to detect the edges of remote sensing images based on Grünwald–Letnikov fractional difference and Otsu threshold. First, a convolution difference mask with two parameters in four directions is constructed by using the definition of the Grünwald–Letnikov fractional derivative. Then, the mask is convolved with the gray image of the remote sensing image, and the edge detection image is obtained by binarization with Otsu threshold. Finally, the influence of two parameters and threshold values on detection results is discussed. Compared with the results of other detectors on the NWPU VHR-10 dataset, it is found that the algorithm not only has good visual effect but also shows good performance in quantitative evaluation indicators (binary graph similarity and edge pixel ratio).
{"title":"Edge detection of remote sensing image based on Grünwald-Letnikov fractional difference and Otsu threshold","authors":"Chao Chen, Hua Kong, Bin Wu","doi":"10.3934/era.2023066","DOIUrl":"https://doi.org/10.3934/era.2023066","url":null,"abstract":"With the development of remote sensing technology, the resolution of remote sensing images is improving, and the presentation of geomorphic information is becoming more and more abundant, the difficulty of identifying and extracting edge information is also increasing. This paper demonstrates an algorithm to detect the edges of remote sensing images based on Grünwald–Letnikov fractional difference and Otsu threshold. First, a convolution difference mask with two parameters in four directions is constructed by using the definition of the Grünwald–Letnikov fractional derivative. Then, the mask is convolved with the gray image of the remote sensing image, and the edge detection image is obtained by binarization with Otsu threshold. Finally, the influence of two parameters and threshold values on detection results is discussed. Compared with the results of other detectors on the NWPU VHR-10 dataset, it is found that the algorithm not only has good visual effect but also shows good performance in quantitative evaluation indicators (binary graph similarity and edge pixel ratio).","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70244415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The application of waste rubber powder (WRP) for asphalt pavement could achieve the harmless and resourceful utilization of solid waste, but the storage stability of waste rubber powder modified asphalt (RA) is one of the main problems restricting its application. Existing studies have demonstrated that graphene could enhance the storage stability of RA, but graphene's size effect on the modifying effect and its corresponding mechanism are still uncertain. In this research, the effects of graphene microstructural properties (i.e., molecular size and layer number) on the storage stability of RA were investigated by storage stability testing, dynamic shear rheometry (DSR) testing and fluorescence microscopy (FM) testing, in combination with molecular dynamics simulation (MD). The experimental results indicated that graphene improved the storage stability of RA significantly, with few-layer graphene being more effective in enhancing it. MD was used to investigate the graphene size effect on RA in compatibility, intermolecular binding energy and structural stability of the system. The simulation results revealed that small-sized graphene molecules were more compatible with RA. Meanwhile, few-layer, small-sized graphene can provide higher binding energy and better enhancement of storage stability of RA. The number of graphene layers mainly influences the binding energy rather than solubility parameters. The relative concentration distribution results demonstrated that graphene facilitated the spatial distribution of asphaltenes, rubber components and light components. This research provides theoretical support for the rational selection of microstructural properties of graphene to improve the modified asphalt storage stability performance.
{"title":"Study on the storage stability performance enhancement mechanism of graphene on rubber-modified asphalt based on size effect","authors":"Yutong Xie, Yingli Gao, M. Liao, Weiwei Tian","doi":"10.3934/era.2023105","DOIUrl":"https://doi.org/10.3934/era.2023105","url":null,"abstract":"The application of waste rubber powder (WRP) for asphalt pavement could achieve the harmless and resourceful utilization of solid waste, but the storage stability of waste rubber powder modified asphalt (RA) is one of the main problems restricting its application. Existing studies have demonstrated that graphene could enhance the storage stability of RA, but graphene's size effect on the modifying effect and its corresponding mechanism are still uncertain. In this research, the effects of graphene microstructural properties (i.e., molecular size and layer number) on the storage stability of RA were investigated by storage stability testing, dynamic shear rheometry (DSR) testing and fluorescence microscopy (FM) testing, in combination with molecular dynamics simulation (MD). The experimental results indicated that graphene improved the storage stability of RA significantly, with few-layer graphene being more effective in enhancing it. MD was used to investigate the graphene size effect on RA in compatibility, intermolecular binding energy and structural stability of the system. The simulation results revealed that small-sized graphene molecules were more compatible with RA. Meanwhile, few-layer, small-sized graphene can provide higher binding energy and better enhancement of storage stability of RA. The number of graphene layers mainly influences the binding energy rather than solubility parameters. The relative concentration distribution results demonstrated that graphene facilitated the spatial distribution of asphaltenes, rubber components and light components. This research provides theoretical support for the rational selection of microstructural properties of graphene to improve the modified asphalt storage stability performance.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70244632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper considers blow-up and global existence for a semilinear space-time fractional pseudo-parabolic equation with nonlinear memory in a bounded domain. We determine the critical exponents of the Cauchy problem when $ alpha < gamma $ and $ alphage gamma, $ respectively. The results obtained in this study are noteworthy extension to the results of time-fractional differential equation. The critical exponent is consistent with the corresponding Cauchy problem for the time-fractional differential equation with nonlinear memory, which illustrates that the diffusion effect of the third order term is not strong enough to change the critical exponents.
{"title":"The critical exponents for a semilinear fractional pseudo-parabolic equation with nonlinear memory in a bounded domain","authors":"Yaning Li, Yuting Yang","doi":"10.3934/era.2023129","DOIUrl":"https://doi.org/10.3934/era.2023129","url":null,"abstract":"This paper considers blow-up and global existence for a semilinear space-time fractional pseudo-parabolic equation with nonlinear memory in a bounded domain. We determine the critical exponents of the Cauchy problem when $ alpha < gamma $ and $ alphage gamma, $ respectively. The results obtained in this study are noteworthy extension to the results of time-fractional differential equation. The critical exponent is consistent with the corresponding Cauchy problem for the time-fractional differential equation with nonlinear memory, which illustrates that the diffusion effect of the third order term is not strong enough to change the critical exponents.","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"6 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70244749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, for given mass $ m > 0 $, we focus on the existence and nonexistence of constrained minimizers of the energy functional begin{document}$ begin{equation*} I(u): = frac{a}{2}int_{mathbb{R}^3}left|nabla uright|^2dx+frac{b}{4}left(int_{mathbb{R}^3}left|nabla uright|^2dxright)^2-int_{mathbb{R}^3}F(u)dx end{equation*} $end{document} on $ S_m: = left{uin H^1(mathbb{R}^3):, |u|^2_2 = mright}, $where $ a, b > 0 $ and $ F $ satisfies the almost optimal mass subcritical growth assumptions. We also establish the relationship between the normalized ground state solutions and the ground state to the action functional $ I(u)-frac{lambda}{2}|u|_2^2 $. Our results extend, nontrivially, the ones in Shibata (Manuscripta Math. 143 (2014) 221–237) and Jeanjean and Lu (Calc. Var. 61 (2022) 214) to the Kirchhoff type equations, and generalize and sharply improve the ones in Ye (Math. Methods. Appl. Sci. 38 (2015) 2603–2679) and Chen et al. (Appl. Math. Optim. 84 (2021) 773–806).
In this paper, for given mass $ m > 0 $, we focus on the existence and nonexistence of constrained minimizers of the energy functional begin{document}$ begin{equation*} I(u): = frac{a}{2}int_{mathbb{R}^3}left|nabla uright|^2dx+frac{b}{4}left(int_{mathbb{R}^3}left|nabla uright|^2dxright)^2-int_{mathbb{R}^3}F(u)dx end{equation*} $end{document} on $ S_m: = left{uin H^1(mathbb{R}^3):, |u|^2_2 = mright}, $where $ a, b > 0 $ and $ F $ satisfies the almost optimal mass subcritical growth assumptions. We also establish the relationship between the normalized ground state solutions and the ground state to the action functional $ I(u)-frac{lambda}{2}|u|_2^2 $. Our results extend, nontrivially, the ones in Shibata (Manuscripta Math. 143 (2014) 221–237) and Jeanjean and Lu (Calc. Var. 61 (2022) 214) to the Kirchhoff type equations, and generalize and sharply improve the ones in Ye (Math. Methods. Appl. Sci. 38 (2015) 2603–2679) and Chen et al. (Appl. Math. Optim. 84 (2021) 773–806).
{"title":"On constrained minimizers for Kirchhoff type equations with Berestycki-Lions type mass subcritical conditions","authors":"Jing Hu, Jijiang Sun$ ^{} $","doi":"10.3934/era.2023131","DOIUrl":"https://doi.org/10.3934/era.2023131","url":null,"abstract":"In this paper, for given mass $ m > 0 $, we focus on the existence and nonexistence of constrained minimizers of the energy functional begin{document}$ begin{equation*} I(u): = frac{a}{2}int_{mathbb{R}^3}left|nabla uright|^2dx+frac{b}{4}left(int_{mathbb{R}^3}left|nabla uright|^2dxright)^2-int_{mathbb{R}^3}F(u)dx end{equation*} $end{document} on $ S_m: = left{uin H^1(mathbb{R}^3):, |u|^2_2 = mright}, $where $ a, b > 0 $ and $ F $ satisfies the almost optimal mass subcritical growth assumptions. We also establish the relationship between the normalized ground state solutions and the ground state to the action functional $ I(u)-frac{lambda}{2}|u|_2^2 $. Our results extend, nontrivially, the ones in Shibata (Manuscripta Math. 143 (2014) 221–237) and Jeanjean and Lu (Calc. Var. 61 (2022) 214) to the Kirchhoff type equations, and generalize and sharply improve the ones in Ye (Math. Methods. Appl. Sci. 38 (2015) 2603–2679) and Chen et al. (Appl. Math. Optim. 84 (2021) 773–806).","PeriodicalId":48554,"journal":{"name":"Electronic Research Archive","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70244821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：