非线性SCHR?DINGER-MAXWELL方程的基态解
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摘要
本文研究了schr?dinger-Maxwell方程基态解存在性的问题.在V,K,f,g满足文中定理1.1的假设条件下,利用山路定理的方法,获得了系统(NSM)的基态解这一结果,推广了文献[1]中0
In this paper, we study the existence of ground state solution for the Schr?dingerMaxwell equations. Under some assumptions of Theorem 1.1 about V,K and f, g, by using mountain pass theorem, we get the ground state solution for(NSM), we promote the conclusion of the first reference with 0 < p < 1 and the second reference about high energy solution.
引文
[1] Sun Juntao. Infinitely many solutions for a class of sublinear Schrodinger-Maxwell equations[J]. J.Math. Anal. Appl., 2012, 390(2):514-522.
[2] Li Qingdong, Su Han, Wei Zhongli. Existence of infinitely many large solutions for the nonlinear Schrodinger-Maxwell equations[J]. Nonl. Anal., 2010, 72(11):4264-4270.
[3] Benci V, Fortunato D. An eigenvalue problem for the Schrodinger-Maxwell equations[J]. Topol.Meth. Nonl. Anal., 1998, 11(2):283-293.
[4] D'Aprile T, Mugnai D. Solitary waves for nonlineax Klein-Gordon-Maxwell and Schrodinger-Maxwell equations[J]. Proc. Royal Soc. Edinb., 2004, 134(5):893-906.
[5] Liu Zhisu, Guo Shangjiang, Zhang Ziheng. Existence of ground state solutions for the SchrodingerPoisson systems[J]. Appl. Math. Comput., 2014, 244(7):312-323.
[6] Sun Jijiang, Ma Shiwang. Ground state solutions for some Schrodinger-Poisson system with periodic potentials[J]. J. Diff. Equ., 2016, 260(1):2119-2149.
[7]方立婉,黄文念,谢苏静.一类非线性schrodinger-Maxwell方程在R~3的基态解[J].数学的实践与认识,2017, 47(18):268-273.
[8] Huang Wennian, Tang Xianhua. Ground-state solutions for asymptotically cubic SchrodingerMaxwell equations[J]. Mediterranean J. Math., 2016, 13(2):3469-3481.
[9] Tang Xianhua. Non-Nehari manifold method for asymptotically linear Schrodinger equation[J]. J.Austr. Math. Soc., 2015, 98(1):104-116.
[10] Yang Minghai, Han Zhiqing. Existence and multiple results for the nonlinear Schrodinger-Poisson system[J]. Nonl. Anal.:Real World Appl., 2012, 13(3):1093-1101.
[11] Li Puyi, Zhang Qi. Existence of positive solutions to the Schrodinger-Poisson systems without compactness conditions[J]. J. Math. Anal. Appl., 2013, 401(2):754-762.
[12] Zou Wenming. Vaxiant fountain theorems and their applications[J]. Manuscr. Math., 2001, 104(3):343-358.
[13] Yosida K. Functional analysis(6th ed.)[M]. Berlin:Springer-Verlag, 1999.
[14] Willem M. Minimax theorems[M]. Boston:Birkhaser, 1996.
[15] tabinowitz P H. Minimax methods in critical point theory with applications to differential equations[J]. Amer. J. Math., 1986, 65:100.
[2] Li Qingdong, Su Han, Wei Zhongli. Existence of infinitely many large solutions for the nonlinear Schrodinger-Maxwell equations[J]. Nonl. Anal., 2010, 72(11):4264-4270.
[3] Benci V, Fortunato D. An eigenvalue problem for the Schrodinger-Maxwell equations[J]. Topol.Meth. Nonl. Anal., 1998, 11(2):283-293.
[4] D'Aprile T, Mugnai D. Solitary waves for nonlineax Klein-Gordon-Maxwell and Schrodinger-Maxwell equations[J]. Proc. Royal Soc. Edinb., 2004, 134(5):893-906.
[5] Liu Zhisu, Guo Shangjiang, Zhang Ziheng. Existence of ground state solutions for the SchrodingerPoisson systems[J]. Appl. Math. Comput., 2014, 244(7):312-323.
[6] Sun Jijiang, Ma Shiwang. Ground state solutions for some Schrodinger-Poisson system with periodic potentials[J]. J. Diff. Equ., 2016, 260(1):2119-2149.
[7]方立婉,黄文念,谢苏静.一类非线性schrodinger-Maxwell方程在R~3的基态解[J].数学的实践与认识,2017, 47(18):268-273.
[8] Huang Wennian, Tang Xianhua. Ground-state solutions for asymptotically cubic SchrodingerMaxwell equations[J]. Mediterranean J. Math., 2016, 13(2):3469-3481.
[9] Tang Xianhua. Non-Nehari manifold method for asymptotically linear Schrodinger equation[J]. J.Austr. Math. Soc., 2015, 98(1):104-116.
[10] Yang Minghai, Han Zhiqing. Existence and multiple results for the nonlinear Schrodinger-Poisson system[J]. Nonl. Anal.:Real World Appl., 2012, 13(3):1093-1101.
[11] Li Puyi, Zhang Qi. Existence of positive solutions to the Schrodinger-Poisson systems without compactness conditions[J]. J. Math. Anal. Appl., 2013, 401(2):754-762.
[12] Zou Wenming. Vaxiant fountain theorems and their applications[J]. Manuscr. Math., 2001, 104(3):343-358.
[13] Yosida K. Functional analysis(6th ed.)[M]. Berlin:Springer-Verlag, 1999.
[14] Willem M. Minimax theorems[M]. Boston:Birkhaser, 1996.
[15] tabinowitz P H. Minimax methods in critical point theory with applications to differential equations[J]. Amer. J. Math., 1986, 65:100.