一类SchrÖdinger-Maxwell系统的多解
Multiple Solutions of a Class of SchrÖdinger-Maxwell System
DOI: 10.12677/AAM.2022.117445, PDF,    国家自然科学基金支持
作者: 刘林祥, 曾 晶*：福建师范大学，数学与统计学院，福建 福州
关键词: SchrÖdinger-Maxwell系统；Ekeland变分原理；山路定理；多重正解；SchrÖdinger-Maxwell System； Ekeland’s Variational Principle； Mountain Pass Theorem； Multiple Positive Solution
摘要: 本文主要研究一类Schrödinger-Maxwell系统，在一定条件下利用临界点理论中的Ekeland变分原理和山路定理证得该系统存在两个正解，并且其中一个解是正能量解，另一个解是负能量解。
Abstract: This paper mainly studies a class of Schrödinger-Maxwell system. Under certain conditions, using the Ekeland’s variational principle and Mountain Pass theorem, it is proved that the system has two positive solutions, one of which is a positive energy solution and the other is a negative energy solu-tion.
文章引用：刘林祥, 曾晶. 一类SchrÖdinger-Maxwell系统的多解[J]. 应用数学进展, 2022, 11(7): 4188-4197. https://doi.org/10.12677/AAM.2022.117445

参考文献

[1] Vaira, G. (2011) Ground States for Schrödinger-Poisson Type Systems. Ricerche di Matematica, 60, 263-297. [Google Scholar] [CrossRef] 
[2] He, X.M. (2011) Multiplicity and Concentration of Positive Solu-tions for the Schrödinger-Poisson Equations. Zeitschrift für angewandte Mathematik und Physik, 62, 869-889. [Google Scholar] [CrossRef] 
[3] Sun, J. and Ma, S. (2016) Ground State Solutions for Some Schrödinger-Poisson Systems with Periodic Potentials. Journal of Differential Equations, 260, 2119-2149. [Google Scholar] [CrossRef] 
[4] Alves, C.O., Souto, M.A.S. and Soares, S.H.M. (2017) A Sign-Changing Solution for the Schrödinger-Poisson Equation in R3. Rocky Mountain Journal of Mathematics, 47, 1-25. [Google Scholar] [CrossRef] 
[5] Azzollini, A. and Pomponio, A. (2008) Ground State Solutions for the Nonlinear Schrödinger-Maxwell Equations. Journal of Mathematical Analysis and Applications, 345, 90-108. [Google Scholar] [CrossRef] 
[6] Chen, S.J. and Tang, C.L. (2009) High Energy Solutions for the Superlinear Schrödinger-Maxwell Equations. Nonlinear Analysis: Theory, Methods & Applications, 71, 4927-4934. [Google Scholar] [CrossRef] 
[7] Li, Q.D., Su, H. and Wei, Z.L. (2010) Existence of Infinitely Many Large Solutions for the Nonlinear Schrödinger-Maxwell Equations. Nonlinear Analysis: Theory, Methods & Applications, 72, 4264-4270. [Google Scholar] [CrossRef] 
[8] Zhang, F. and Cai, L. (2019) Bound and Ground States for a Class of Schrödinger-Poisson Systems. Boundary Value Problems, 2019, Article No. 126. [Google Scholar] [CrossRef] 
[9] Fang, X.D. (2019) Bound State Solutions for Some Non-Autonomous Asymptotically Cubic Schrödinger-Poisson Systems. Ztschrift für angewandte Mathematik und Physik, 70, Article No. 50. [Google Scholar] [CrossRef] 
[10] Yang, M., Zhao, F. and Ding, Y. (2012) On the Existence of So-lutions for Schrödinger-Maxwell Systems in R3. Rocky Mountain Journal of Mathematics, 42, 1655-1674. [Google Scholar] [CrossRef] 
[11] Salvatore, A. (2006) Multiple Solitary Waves for a Non-Homogeneous Schrödinger-Maxwell System in R3. Advanced Nonlinear Studies, 6, 157-169. [Google Scholar] [CrossRef] 
[12] Bartsch, T. and Wang, Z.Q. (1995) Existence and Multiplicity Results for Some Superlinear Elliptic Problems on RN. Communications in Partial Differential Equations, 20, 1725-1741. [Google Scholar] [CrossRef] 
[13] Zou, W.M. and Schechter, M. (2006) Critical Point Theory and Its Applications. Springer, New York.
[14] d’Avenia, P., Pomponio, A. and Vaira, G. (2011) Infinitely Many Positive Solutions for a Schrödinger-Poisson System. Applied Mathematics Letters, 24, 661-664. [Google Scholar] [CrossRef] 
[15] Benci, V., Fortunato, D., Masiello, A. and Pisani, L. (1999) Soli-tons and the Electromagnetic Field. Mathematische Zeitschrift, 232, 73-102. [Google Scholar] [CrossRef] 

为你推荐