GROUND STATE SOLUTIONS OF NEHARI-POHOZAEV TYPE FOR SCHRODINGER-POISSON PROBLEMS WITH GENERAL POTENTIALS

被引：139

作者：

Tang, Xianhua ^{[1
]}

Chen, Sitong ^{[1
]}

机构：

[1] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2017年 / 37卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Schrodinger-Poisson problem; ground state solution of Nehari-Pohozaev type; the least energy solutions; KLEIN-GORDON-MAXWELL; THOMAS-FERMI; SEMICLASSICAL SOLUTIONS; POSITIVE SOLUTIONS; EQUATIONS; MOLECULES; SYSTEMS; ATOMS; NONLINEARITY; SEQUENCES;

D O I：

10.3934/dcds.2017214

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is dedicated to studying the following Schrodinger-Poisson problem {-Delta u + V(x)u + phi u - f(u), x is an element of R-3 -Delta phi + u(2), x is an element of R-3 , where V(x) is weakly differentiable and f E is an element of C(R, R). By introducing some new tricks, we prove the above problem admits a ground state solution of Nehari-Pohozaev type and a least energy solution under mild assumptions on V and f. Our results generalize and improve the ones in [D. Ruiz, J. Funct. Anal. 237 (2006) 655-674], [J.J. Sun, S.W. Ma, J. Differential Equations 260 (2016) 2119-2149] and some related literature.

引用

页码：4973 / 5002

页数：30

共 35 条

[1] Multibump solutions of nonlinear periodic Schrodinger equations in a degenerate setting [J].

Ackermann, N ;

Weth, T .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2005, 7 (03) :269-298

[2] Multiple bound states for the Schrodinger-Poisson problem [J].

Ambrosetti, Antonio ;

Ruiz, David .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2008, 10 (03) :391-404

[3]

[Anonymous], 1997, Minimax theorems

[4] Ground state solutions for the nonlinear Schrodinger-Maxwell equations [J].

Azzollini, A. ;

Pomponio, A. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 345 (01) :90-108

[5] Solitary waves of the nonlinear Klein-Gordon equation coupled with the Maxwell equations [J].

Benci, V ;

Fortunato, D .

REVIEWS IN MATHEMATICAL PHYSICS, 2002, 14 (04) :409-420

[6]

Benci V., 1998, Topol. Methods Nonlinear Anal., V11, P283

[7] THE THOMAS-FERMI-VONWEIZSACKER THEORY OF ATOMS AND MOLECULES [J].

BENGURIA, R ;

BREZIS, H ;

LIEB, EH .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1981, 79 (02) :167-180

[8] BINDING OF ATOMS AND STABILITY OF MOLECULES IN HARTREE AND THOMAS-FERMI TYPE THEORIES .1. A NECESSARY AND SUFFICIENT CONDITION FOR THE STABILITY OF GENERAL MOLECULAR-SYSTEMS [J].

CATTO, I ;

LIONS, PL .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1992, 17 (7-8) :1051-1110

[9] Positive solutions for some non-autonomous Schrodinger-Poisson systems [J].

Cerami, Giovanna ;

Vaira, Giusi .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 248 (03) :521-543

[10] Nehari Type Ground State Solutions for Asymptotically Periodic Schrodinger-PoissonSystems [J].

Chen, Sitong ;

Tang, Xianhua .

TAIWANESE JOURNAL OF MATHEMATICS, 2017, 21 (02) :363-383

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