Pub Date : 2024-11-22DOI: 10.1016/j.aml.2024.109389
Anbiao Zeng, Guangze Gu
We consider the following fractional Schrödinger–Poisson system where is a fixed constant, is continuous, sublinear at the origin and subcritical at infinity. Applying the Clark’s theorem and truncation method, we can obtain a sequence of negative energy solutions.
{"title":"Infinitely many negative energy solutions for fractional Schrödinger–Poisson systems","authors":"Anbiao Zeng, Guangze Gu","doi":"10.1016/j.aml.2024.109389","DOIUrl":"10.1016/j.aml.2024.109389","url":null,"abstract":"<div><div>We consider the following fractional Schrödinger–Poisson system <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup><mi>u</mi><mo>+</mo><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>u</mi><mo>+</mo><mi>ϕ</mi><mi>u</mi><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup><mi>ϕ</mi><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>where <span><math><mrow><mi>s</mi><mo>∈</mo><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> is a fixed constant, <span><math><mi>f</mi></math></span> is continuous, sublinear at the origin and subcritical at infinity. Applying the Clark’s theorem and truncation method, we can obtain a sequence of negative energy solutions.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109389"},"PeriodicalIF":2.9,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142723211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-21DOI: 10.1016/j.aml.2024.109388
Zhihao Sheng , Yang Liu , Yonghai Li
In this article, we propose a novel second-order shifted convolution quadrature (SCQ) formula including both a shifted parameter and a new variable parameter . We prove the second-order truncation error of the novel formula for the time-fractional derivative, and derive the nonnegative property of the formula’s weights. Combining the novel formula with the finite element method, we develop a high order numerical scheme for fractional mobile/immobile transport equations. Furthermore, we analyze the stability and error estimate of the numerical method. We present numerical tests to further validate our theoretical results.
{"title":"A double-parameter shifted convolution quadrature formula and its application to fractional mobile/immobile transport equations","authors":"Zhihao Sheng , Yang Liu , Yonghai Li","doi":"10.1016/j.aml.2024.109388","DOIUrl":"10.1016/j.aml.2024.109388","url":null,"abstract":"<div><div>In this article, we propose a novel second-order shifted convolution quadrature (SCQ) formula including both a shifted parameter <span><math><mi>θ</mi></math></span> and a new variable parameter <span><math><mi>δ</mi></math></span>. We prove the second-order truncation error of the novel formula for the time-fractional derivative, and derive the nonnegative property of the formula’s weights. Combining the novel formula with the finite element method, we develop a high order numerical scheme for fractional mobile/immobile transport equations. Furthermore, we analyze the stability and error estimate of the numerical method. We present numerical tests to further validate our theoretical results.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109388"},"PeriodicalIF":2.9,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-19DOI: 10.1016/j.aml.2024.109380
Shubin Yu
We consider the existence of positive solutions for following Kirchhoff equation where , is the exterior of the unit ball in and . It is well-known that if , by standard minimization method on the Nehari manifold, one can obtain a positive radial solution. In present paper, we prove the existence of positive radial solutions for . This is the first contribution to the Kirchhoff equation in exterior domains provided that
{"title":"A new observation on the positive solutions for Kirchhoff equations in the exterior of a ball","authors":"Shubin Yu","doi":"10.1016/j.aml.2024.109380","DOIUrl":"10.1016/j.aml.2024.109380","url":null,"abstract":"<div><div>We consider the existence of positive solutions for following Kirchhoff equation <span><math><mfenced><mrow><mtable><mtr><mtd><mo>−</mo><mfenced><mrow><mi>a</mi><mo>+</mo><mi>b</mi><msub><mrow><mo>∫</mo></mrow><mrow><mi>Ω</mi></mrow></msub><msup><mrow><mrow><mo>|</mo><mo>∇</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mi>d</mi><mi>x</mi></mrow></mfenced><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>u</mi><mo>=</mo><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi></mtd><mtd><mtext>in</mtext><mspace></mspace><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mo>=</mo><mn>0</mn></mtd><mtd><mtext>on</mtext><mspace></mspace><mi>∂</mi><mi>Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span> where <span><math><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>></mo><mn>0</mn></mrow></math></span>, <span><math><mrow><mi>Ω</mi><mo>=</mo><mrow><mo>{</mo><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>:</mo><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow><mo>></mo><mn>1</mn><mo>}</mo></mrow></mrow></math></span> is the exterior of the unit ball in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> and <span><math><mrow><mi>N</mi><mo>≥</mo><mn>2</mn></mrow></math></span>. It is well-known that if <span><math><mrow><mn>4</mn><mo><</mo><mi>p</mi><mo><</mo><mi>∞</mi></mrow></math></span>, by standard minimization method on the Nehari manifold, one can obtain a positive radial solution. In present paper, we prove the existence of positive radial solutions for <span><math><mrow><mn>2</mn><mo><</mo><mi>p</mi><mo>≤</mo><mn>4</mn></mrow></math></span>. This is the first contribution to the Kirchhoff equation in exterior domains provided that <span><math><mrow><mn>2</mn><mo><</mo><mi>p</mi><mo>≤</mo><mn>4</mn><mo>.</mo></mrow></math></span></div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109380"},"PeriodicalIF":2.9,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-19DOI: 10.1016/j.aml.2024.109383
Xin Zhang , Xiaofeng Li , Guoli Ma
The building of the national communication infrastructure and growing demand for data traffic both depend heavily on the advancement of optical soliton communication technology. In particular, by studying the interaction of optical solitons, some methods of controlling optical solitons can be explored to design more stable and efficient optical communication systems. In this paper, the interactions between optical solitons are studied based on the theory of generalized Schrödinger–Hirota equation. By studying the amplitude ratio, spacing and phase difference of the optical solitons, the interactions between the optical solitons occurring in the optical fiber transmission process are attenuated. The noninteraction transmission of optical solitons are realized with small spacing between them. The conclusions of this paper are not only of great significance for the in-depth understanding of the nature of optical soliton interactions, but also of great practical value for promoting the application of optical solitons in optical communications and other fields.
{"title":"Optical soliton noninteraction transmission in optical communication systems","authors":"Xin Zhang , Xiaofeng Li , Guoli Ma","doi":"10.1016/j.aml.2024.109383","DOIUrl":"10.1016/j.aml.2024.109383","url":null,"abstract":"<div><div>The building of the national communication infrastructure and growing demand for data traffic both depend heavily on the advancement of optical soliton communication technology. In particular, by studying the interaction of optical solitons, some methods of controlling optical solitons can be explored to design more stable and efficient optical communication systems. In this paper, the interactions between optical solitons are studied based on the theory of generalized Schrödinger–Hirota equation. By studying the amplitude ratio, spacing and phase difference of the optical solitons, the interactions between the optical solitons occurring in the optical fiber transmission process are attenuated. The noninteraction transmission of optical solitons are realized with small spacing between them. The conclusions of this paper are not only of great significance for the in-depth understanding of the nature of optical soliton interactions, but also of great practical value for promoting the application of optical solitons in optical communications and other fields.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109383"},"PeriodicalIF":2.9,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-19DOI: 10.1016/j.aml.2024.109386
Xiaohua Jing , Junxiong Jia , Xueli Song
This article is concerned with the uniqueness of simultaneously determining the fractional order of the derivative in time, diffusion coefficient, and Robin coefficient, in one-dimensional time-fractional diffusion equations with derivative order and non-zero boundary conditions. The measurement data, which is the solution to the initial–boundary value problem, is observed at a single boundary point over a finite time interval. Based on the expansion of eigenfunctions for the solution to the forward problem and the asymptotic properties of the Mittag-Leffler function, the uniqueness of the fractional order is established. Subsequently, the uniqueness of the eigenvalues and the absolute value of the eigenfunction evaluated at for the associated operator are demonstrated. Then, the uniqueness of identifying the diffusion coefficient and the Robin coefficient is proven via an inverse boundary spectral analysis for the eigenvalue problem of the spatial differential operator. The results show that the uniqueness of three parameters can be simultaneously determined using limited boundary observations at a single spatial endpoint over a finite time interval, without imposing any constraints on the eigenfunctions of the spatial differential operator.
{"title":"Simultaneous uniqueness identification of the fractional order and diffusion coefficient in a time-fractional diffusion equation","authors":"Xiaohua Jing , Junxiong Jia , Xueli Song","doi":"10.1016/j.aml.2024.109386","DOIUrl":"10.1016/j.aml.2024.109386","url":null,"abstract":"<div><div>This article is concerned with the uniqueness of simultaneously determining the fractional order of the derivative in time, diffusion coefficient, and Robin coefficient, in one-dimensional time-fractional diffusion equations with derivative order <span><math><mrow><mi>α</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> and non-zero boundary conditions. The measurement data, which is the solution to the initial–boundary value problem, is observed at a single boundary point over a finite time interval. Based on the expansion of eigenfunctions for the solution to the forward problem and the asymptotic properties of the Mittag-Leffler function, the uniqueness of the fractional order is established. Subsequently, the uniqueness of the eigenvalues and the absolute value of the eigenfunction evaluated at <span><math><mrow><mi>x</mi><mo>=</mo><mn>0</mn></mrow></math></span> for the associated operator are demonstrated. Then, the uniqueness of identifying the diffusion coefficient and the Robin coefficient is proven via an inverse boundary spectral analysis for the eigenvalue problem of the spatial differential operator. The results show that the uniqueness of three parameters can be simultaneously determined using limited boundary observations at a single spatial endpoint over a finite time interval, without imposing any constraints on the eigenfunctions of the spatial differential operator.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109386"},"PeriodicalIF":2.9,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-19DOI: 10.1016/j.aml.2024.109381
Juan Gerardo Alcázar , Michal Bizzarri , Miroslav Lávička , Jan Vršek
We prove that, under generic conditions, the covariance matrix of a 3D point cloud with rotational symmetry has a simple eigenvalue, whose associated eigenvector provides the direction of the axis of rotation, and a double eigenvalue. The direction of the axis of rotation can also be computed from higher order tensors related to the point cloud, which is useful in pathological cases. This leads to a very simple algorithm for detecting rotational symmetry and computing the axis of rotation.
{"title":"Rotational symmetries of 3D point clouds using the covariance matrix and higher-order tensors","authors":"Juan Gerardo Alcázar , Michal Bizzarri , Miroslav Lávička , Jan Vršek","doi":"10.1016/j.aml.2024.109381","DOIUrl":"10.1016/j.aml.2024.109381","url":null,"abstract":"<div><div>We prove that, under generic conditions, the covariance matrix of a 3D point cloud with rotational symmetry has a simple eigenvalue, whose associated eigenvector provides the direction of the axis of rotation, and a double eigenvalue. The direction of the axis of rotation can also be computed from higher order tensors related to the point cloud, which is useful in pathological cases. This leads to a very simple algorithm for detecting rotational symmetry and computing the axis of rotation.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109381"},"PeriodicalIF":2.9,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-19DOI: 10.1016/j.aml.2024.109387
Fiona McIntosh, Lily Amirzadeh, Brian E. Moore
Explicit, conformal symplectic, exponential time differencing (ETD) methods have numerous advantages over other well-known and commonly used methods, including structure-preservation, high stability, ease of implementation, and computational efficiency. Such methods are constructed with second and fourth order accuracy through composition techniques using a simple first order scheme. For modeling Josephson Junctions, these ETD schemes regularly exhibit the best balance of efficiency and accuracy when compared to other commonly used methods.
{"title":"Structure-preserving exponential time differencing methods for modeling Josephson Junctions","authors":"Fiona McIntosh, Lily Amirzadeh, Brian E. Moore","doi":"10.1016/j.aml.2024.109387","DOIUrl":"10.1016/j.aml.2024.109387","url":null,"abstract":"<div><div>Explicit, conformal symplectic, exponential time differencing (ETD) methods have numerous advantages over other well-known and commonly used methods, including structure-preservation, high stability, ease of implementation, and computational efficiency. Such methods are constructed with second and fourth order accuracy through composition techniques using a simple first order scheme. For modeling Josephson Junctions, these ETD schemes regularly exhibit the best balance of efficiency and accuracy when compared to other commonly used methods.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109387"},"PeriodicalIF":2.9,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-15DOI: 10.1016/j.aml.2024.109369
Ya Li, Xiaolei Yuan, Hongyan Ma
Based on the phase-field theory, a new wetting boundary condition (WBC) scheme is proposed to describe the fluid–solid interaction of binary fluids. Different from the common linear, cubic and sine form of surface energy wetting conditions, we adopt a mixed cubic and sine form of free energy in the present scheme. Two conditions are given to ensure that the spurious film at the solid surface disappears and the reasonable boundary condition is obtained. Combined with the wetting scheme and lattice Boltzmann (LB) method based on phase-field theory, numerical simulation of droplet spreading on a cylindrical surface is carried out to verify the performance of the present WBC. It is found that the present wetting scheme can offer considerable accuracy for predicting a static contact angle, which means that it can be used to study the wetting boundary problems of binary fluids.
{"title":"Alternative wetting boundary condition for binary fluids based on phase-field lattice Boltzmann method","authors":"Ya Li, Xiaolei Yuan, Hongyan Ma","doi":"10.1016/j.aml.2024.109369","DOIUrl":"10.1016/j.aml.2024.109369","url":null,"abstract":"<div><div>Based on the phase-field theory, a new wetting boundary condition (WBC) scheme is proposed to describe the fluid–solid interaction of binary fluids. Different from the common linear, cubic and sine form of surface energy wetting conditions, we adopt a mixed cubic and sine form of free energy in the present scheme. Two conditions are given to ensure that the spurious film at the solid surface disappears and the reasonable boundary condition is obtained. Combined with the wetting scheme and lattice Boltzmann (LB) method based on phase-field theory, numerical simulation of droplet spreading on a cylindrical surface is carried out to verify the performance of the present WBC. It is found that the present wetting scheme can offer considerable accuracy for predicting a static contact angle, which means that it can be used to study the wetting boundary problems of binary fluids.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"162 ","pages":"Article 109369"},"PeriodicalIF":2.9,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142696455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study we consider a spline-based collocation method to approximate the solution of fractional convection–diffusion equations which include fractional derivatives in both space and time. This kind of fractional differential equations are valuable for modeling various real-world phenomena across different scientific disciplines such as finance, physics, biology and engineering.
The model includes the fractional derivatives of order between 0 and 1 in space and time, considered in the Caputo sense and the spatial fractional diffusion, represented by the Riesz–Caputo derivative (fractional order between 1 and 2). We propose and analyze a collocation method that employs a B-spline representation of the solution. This method exploits the symmetry properties of both the spline basis functions and the Riesz–Caputo operator, leading to an efficient approach for solving the fractional differential problem. We discuss the advantages of using Greville Abscissae as collocation points, and compare this choice with other possible distributions of points. Numerical experiments are presented to demonstrate the effectiveness of the proposed method.
{"title":"A spline-based framework for solving the space–time fractional convection–diffusion problem","authors":"Chiara Sorgentone , Enza Pellegrino , Francesca Pitolli","doi":"10.1016/j.aml.2024.109370","DOIUrl":"10.1016/j.aml.2024.109370","url":null,"abstract":"<div><div>In this study we consider a spline-based collocation method to approximate the solution of fractional convection–diffusion equations which include fractional derivatives in both space and time. This kind of fractional differential equations are valuable for modeling various real-world phenomena across different scientific disciplines such as finance, physics, biology and engineering.</div><div>The model includes the fractional derivatives of order between 0 and 1 in space and time, considered in the Caputo sense and the spatial fractional diffusion, represented by the Riesz–Caputo derivative (fractional order between 1 and 2). We propose and analyze a collocation method that employs a B-spline representation of the solution. This method exploits the symmetry properties of both the spline basis functions and the Riesz–Caputo operator, leading to an efficient approach for solving the fractional differential problem. We discuss the advantages of using Greville Abscissae as collocation points, and compare this choice with other possible distributions of points. Numerical experiments are presented to demonstrate the effectiveness of the proposed method.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"161 ","pages":"Article 109370"},"PeriodicalIF":2.9,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-12DOI: 10.1016/j.aml.2024.109368
Rong Zhang, Shuai Yao, Juntao Sun
In this paper, we study a class of Schrödinger–Bopp–Podolsky systems with a negative potential in . By using Mountain-Pass argument and detailed analysis of the energy level value, we obtain a normalized solution with positive energy under suitable assumptions on . Moreover, we also prove that there is no normalized solutions with negative energy.
{"title":"Normalized solutions for Schrödinger–Bopp–Podolsky system with a negative potential","authors":"Rong Zhang, Shuai Yao, Juntao Sun","doi":"10.1016/j.aml.2024.109368","DOIUrl":"10.1016/j.aml.2024.109368","url":null,"abstract":"<div><div>In this paper, we study a class of Schrödinger–Bopp–Podolsky systems with a negative potential <span><math><mrow><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. By using Mountain-Pass argument and detailed analysis of the energy level value, we obtain a normalized solution with positive energy under suitable assumptions on <span><math><mrow><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span>. Moreover, we also prove that there is no normalized solutions with negative energy.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"161 ","pages":"Article 109368"},"PeriodicalIF":2.9,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号