Pub Date : 2024-05-10DOI: 10.1186/s13661-024-01864-0
Abdelbaki Choucha, Mohamed Haiour, Salah Boulaaras
In this work, we consider a quasilinear system of viscoelastic equations with dispersion, source, and variable exponents. Under suitable assumptions on the initial data and the relaxation functions, we obtained that the solution of the system is global and bounded. Next, the blow-up is proved with negative initial energy. After that, the exponential growth of solutions is showed with positive initial energy, and by using an integral inequality due to Komornik, the general decay result is obtained in the case of absence of the source term.
{"title":"On a class of a coupled nonlinear viscoelastic Kirchhoff equations variable-exponents: global existence, blow up, growth and decay of solutions","authors":"Abdelbaki Choucha, Mohamed Haiour, Salah Boulaaras","doi":"10.1186/s13661-024-01864-0","DOIUrl":"https://doi.org/10.1186/s13661-024-01864-0","url":null,"abstract":"In this work, we consider a quasilinear system of viscoelastic equations with dispersion, source, and variable exponents. Under suitable assumptions on the initial data and the relaxation functions, we obtained that the solution of the system is global and bounded. Next, the blow-up is proved with negative initial energy. After that, the exponential growth of solutions is showed with positive initial energy, and by using an integral inequality due to Komornik, the general decay result is obtained in the case of absence of the source term.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"133 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140936232","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}
Pub Date : 2024-05-03DOI: 10.1186/s13661-024-01861-3
Elkhateeb S. Aly, M. Latha Maheswari, K. S. Keerthana Shri, Waleed Hamali
This article investigates sufficient conditions for the existence and uniqueness of solutions to the ψ-Hilfer sequential type pantograph fractional boundary value problem. Considering the system depends on a lower-order fractional derivative of an unknown function, the study is carried out in a special working space. Standard fixed point theorems such as the Banach contraction principle and Krasnosel’skii’s fixed point theorem are applied to prove the uniqueness and the existence of a solution, respectively. Finally, an example demonstrating our results with numerical simulations is presented.
{"title":"A novel approach on the sequential type ψ-Hilfer pantograph fractional differential equation with boundary conditions","authors":"Elkhateeb S. Aly, M. Latha Maheswari, K. S. Keerthana Shri, Waleed Hamali","doi":"10.1186/s13661-024-01861-3","DOIUrl":"https://doi.org/10.1186/s13661-024-01861-3","url":null,"abstract":"This article investigates sufficient conditions for the existence and uniqueness of solutions to the ψ-Hilfer sequential type pantograph fractional boundary value problem. Considering the system depends on a lower-order fractional derivative of an unknown function, the study is carried out in a special working space. Standard fixed point theorems such as the Banach contraction principle and Krasnosel’skii’s fixed point theorem are applied to prove the uniqueness and the existence of a solution, respectively. Finally, an example demonstrating our results with numerical simulations is presented.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"4 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140826969","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}
Pub Date : 2024-04-19DOI: 10.1186/s13661-024-01860-4
Zhaoying Wei, Zhijie Hu, Yuewen Xiang
In this paper we are concerned with an inverse problem with Robin boundary conditions, which states that, when the potential on $[0,1/2]$ and the coefficient at the left end point are known a priori, a full spectrum uniquely determines its potential on the whole interval and the coefficient at the right end point. We shall give a new method for reconstructing the potential for this problem in terms of the Mittag-Leffler decomposition of entire functions associated with this problem. The new reconstructing method also deduces a necessary and sufficient condition for the existence issue.
{"title":"Reconstruction of the solution of inverse Sturm–Liouville problem","authors":"Zhaoying Wei, Zhijie Hu, Yuewen Xiang","doi":"10.1186/s13661-024-01860-4","DOIUrl":"https://doi.org/10.1186/s13661-024-01860-4","url":null,"abstract":"In this paper we are concerned with an inverse problem with Robin boundary conditions, which states that, when the potential on $[0,1/2]$ and the coefficient at the left end point are known a priori, a full spectrum uniquely determines its potential on the whole interval and the coefficient at the right end point. We shall give a new method for reconstructing the potential for this problem in terms of the Mittag-Leffler decomposition of entire functions associated with this problem. The new reconstructing method also deduces a necessary and sufficient condition for the existence issue.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"21 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140624543","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}
Pub Date : 2024-04-11DOI: 10.1186/s13661-024-01858-y
Lin Zheng
In this paper, we prove that for certain class of initial data, the corresponding solutions to the 3-D viscous primitive equations blow up in finite time. Specifically, we find a special solution to simplify the 3-D systems, assuming that the pressure function $p(x,y,t)$ is a concave function. We also consider the equations on the line $x=0$ , $y=0$ .
{"title":"Finite-time blowup for the 3-D viscous primitive equations of oceanic and atmospheric dynamics","authors":"Lin Zheng","doi":"10.1186/s13661-024-01858-y","DOIUrl":"https://doi.org/10.1186/s13661-024-01858-y","url":null,"abstract":"In this paper, we prove that for certain class of initial data, the corresponding solutions to the 3-D viscous primitive equations blow up in finite time. Specifically, we find a special solution to simplify the 3-D systems, assuming that the pressure function $p(x,y,t)$ is a concave function. We also consider the equations on the line $x=0$ , $y=0$ .","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"22 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140588114","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}
Pub Date : 2024-04-10DOI: 10.1186/s13661-024-01855-1
Wali Haider, Hüseyin Budak, Asia Shehzadi, Fatih Hezenci, Haibo Chen
In the framework of tempered fractional integrals, we obtain a fundamental identity for differentiable convex functions. By employing this identity, we derive several modifications of fractional Milne inequalities, providing novel extensions to the domain of tempered fractional integrals. The research comprehensively examines significant functional classes, including convex functions, bounded functions, Lipschitzian functions, and functions of bounded variation.
{"title":"A comprehensive study on Milne-type inequalities with tempered fractional integrals","authors":"Wali Haider, Hüseyin Budak, Asia Shehzadi, Fatih Hezenci, Haibo Chen","doi":"10.1186/s13661-024-01855-1","DOIUrl":"https://doi.org/10.1186/s13661-024-01855-1","url":null,"abstract":"In the framework of tempered fractional integrals, we obtain a fundamental identity for differentiable convex functions. By employing this identity, we derive several modifications of fractional Milne inequalities, providing novel extensions to the domain of tempered fractional integrals. The research comprehensively examines significant functional classes, including convex functions, bounded functions, Lipschitzian functions, and functions of bounded variation.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"298 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140587825","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}
Pub Date : 2024-04-09DOI: 10.1186/s13661-024-01859-x
Bayan Bekbolat, Niyaz Tokmagambetov
In this paper, we investigate direct and inverse problems for time-fractional pseudoparabolic equations associated with the Jacobi operator. The existence and uniqueness of the solutions are proven. Also, the stability result of the inverse source problem (ISP) is established.
{"title":"Inverse source problem for the pseudoparabolic equation associated with the Jacobi operator","authors":"Bayan Bekbolat, Niyaz Tokmagambetov","doi":"10.1186/s13661-024-01859-x","DOIUrl":"https://doi.org/10.1186/s13661-024-01859-x","url":null,"abstract":"In this paper, we investigate direct and inverse problems for time-fractional pseudoparabolic equations associated with the Jacobi operator. The existence and uniqueness of the solutions are proven. Also, the stability result of the inverse source problem (ISP) is established.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"6 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140587326","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}
Pub Date : 2024-04-08DOI: 10.1186/s13661-024-01840-8
Xuxin Yang, Piao Liu, Weibing Wang
In this paper, we study the existence, nonexistence, and multiplicity of positive solutions to a nonlinear impulsive Sturm–Liouville boundary value problem with a parameter. By using a variational method, we prove that the problem has at least two positive solutions for the parameter $lambda in (0,Lambda )$ , one positive solution for $lambda =Lambda $ , and no positive solution for $lambda >Lambda $ , where $Lambda >0$ is a constant.
{"title":"Multiplicity and nonexistence of positive solutions to impulsive Sturm–Liouville boundary value problems","authors":"Xuxin Yang, Piao Liu, Weibing Wang","doi":"10.1186/s13661-024-01840-8","DOIUrl":"https://doi.org/10.1186/s13661-024-01840-8","url":null,"abstract":"In this paper, we study the existence, nonexistence, and multiplicity of positive solutions to a nonlinear impulsive Sturm–Liouville boundary value problem with a parameter. By using a variational method, we prove that the problem has at least two positive solutions for the parameter $lambda in (0,Lambda )$ , one positive solution for $lambda =Lambda $ , and no positive solution for $lambda >Lambda $ , where $Lambda >0$ is a constant.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"156 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140587679","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}
Pub Date : 2024-04-04DOI: 10.1186/s13661-024-01857-z
Penghui Lv, Yuan Yuan, Guoguang Lin
The Kirchhoff model is derived from the vibration problem of stretchable strings. This paper focuses on the longtime dynamics of a higher-order $(m_{1},m_{2})$ -coupled Kirchhoff system with higher-order rotational inertia and nonlocal damping. We first obtain the state of the model’s solutions in different spaces through prior estimation. After that, we immediately prove the existence and uniqueness of their solutions in different spaces through the Faedo-Galerkin method. Subsequently, we prove their family of global attractors using the compactness theorem. Finally, we reflect on the subsequent research of the model and point out relevant directions for further research on the model. In this way, we systematically study the longtime dynamics of the higher-order $(m_{1},m_{2})$ -coupled Kirchhoff model with higher-order rotational inertia, thus enriching the relevant findings of higher-order coupled Kirchhoff models and laying a theoretical foundation for future practical applications.
{"title":"Longtime dynamics of solutions for higher-order ((m_{1},m_{2}))-coupled Kirchhoff models with higher-order rotational inertia and nonlocal damping","authors":"Penghui Lv, Yuan Yuan, Guoguang Lin","doi":"10.1186/s13661-024-01857-z","DOIUrl":"https://doi.org/10.1186/s13661-024-01857-z","url":null,"abstract":"The Kirchhoff model is derived from the vibration problem of stretchable strings. This paper focuses on the longtime dynamics of a higher-order $(m_{1},m_{2})$ -coupled Kirchhoff system with higher-order rotational inertia and nonlocal damping. We first obtain the state of the model’s solutions in different spaces through prior estimation. After that, we immediately prove the existence and uniqueness of their solutions in different spaces through the Faedo-Galerkin method. Subsequently, we prove their family of global attractors using the compactness theorem. Finally, we reflect on the subsequent research of the model and point out relevant directions for further research on the model. In this way, we systematically study the longtime dynamics of the higher-order $(m_{1},m_{2})$ -coupled Kirchhoff model with higher-order rotational inertia, thus enriching the relevant findings of higher-order coupled Kirchhoff models and laying a theoretical foundation for future practical applications.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"166 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140602574","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}
Pub Date : 2024-04-02DOI: 10.1186/s13661-024-01849-z
A. M. Mahmoud, D. A. Eisa, R. O. A. Taie, D. A. M. Bakhit
In the present paper, we study stochastic stability and stochastic boundedness for the stochastic differential equation (SDE) with multi-delay of third order. The derived results extend and improve some earlier results in the relevant literature, which are related to the qualitative properties of solutions to third-order delay differential equations (DDEs) and SDEs with multi-delay. Two examples are given to illustrate the results.
{"title":"Asymptotic behaviour and boundedness of solutions for third-order stochastic differential equation with multi-delay","authors":"A. M. Mahmoud, D. A. Eisa, R. O. A. Taie, D. A. M. Bakhit","doi":"10.1186/s13661-024-01849-z","DOIUrl":"https://doi.org/10.1186/s13661-024-01849-z","url":null,"abstract":"In the present paper, we study stochastic stability and stochastic boundedness for the stochastic differential equation (SDE) with multi-delay of third order. The derived results extend and improve some earlier results in the relevant literature, which are related to the qualitative properties of solutions to third-order delay differential equations (DDEs) and SDEs with multi-delay. Two examples are given to illustrate the results.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"17 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140587339","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}
Pub Date : 2024-03-29DOI: 10.1186/s13661-024-01854-2
Ahmad Aloqaily, P. Agilan, K. Julietraja, S. Annadurai, Nabil Mlaiki
The analysis of stability in functional equations (FEs) within neutrosophic normed spaces is a significant challenge due to the inherent uncertainties and complexities involved. This paper proposes a novel approach to address this challenge, offering a comprehensive framework for investigating stability properties in such contexts. Neutrosophic normed spaces are a generalization of traditional normed spaces that incorporate neutrosophic logic. By providing a systematic methodology for addressing stability concerns in neutrosophic normed spaces, our approach facilitates enhanced understanding and control of complex systems characterized by indeterminacy and uncertainty. The primary focus of this research is to propose a novel class of Euler-Lagrange additive FE and investigate its Ulam-Hyers stability in neutrosophic normed spaces. Direct and fixed point techniques are utilized to achieve the required results.
{"title":"A novel stability analysis of functional equation in neutrosophic normed spaces","authors":"Ahmad Aloqaily, P. Agilan, K. Julietraja, S. Annadurai, Nabil Mlaiki","doi":"10.1186/s13661-024-01854-2","DOIUrl":"https://doi.org/10.1186/s13661-024-01854-2","url":null,"abstract":"The analysis of stability in functional equations (FEs) within neutrosophic normed spaces is a significant challenge due to the inherent uncertainties and complexities involved. This paper proposes a novel approach to address this challenge, offering a comprehensive framework for investigating stability properties in such contexts. Neutrosophic normed spaces are a generalization of traditional normed spaces that incorporate neutrosophic logic. By providing a systematic methodology for addressing stability concerns in neutrosophic normed spaces, our approach facilitates enhanced understanding and control of complex systems characterized by indeterminacy and uncertainty. The primary focus of this research is to propose a novel class of Euler-Lagrange additive FE and investigate its Ulam-Hyers stability in neutrosophic normed spaces. Direct and fixed point techniques are utilized to achieve the required results.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"41 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140323483","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}
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