GROUND STATE SOLUTIONS FOR ASYMPTOTICALLY PERIODIC QUASILINEAR SCHRODINGER EQUATIONS WITH CRITICAL GROWTH

被引：8

作者：

Xue, Yanfang ^{[1
,2
]}

Tang, Chunlei ^{[1
]}

机构：

[1] Southwest Univ, Sch Math & Stat, Chongqing 400700, Peoples R China

[2] Xin Yang Normal Univ, Sch Math & Stat, Xinyang 464000, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2018年 / 17卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Asymptotically periodic; Sobolev critical exponent; ground state solution; Nehari manifold; CONCENTRATION-COMPACTNESS PRINCIPLE; CRITICAL SOBOLEV EXPONENTS; ELLIPTIC-EQUATIONS; SOLITON-SOLUTIONS; PERTURBATION METHOD; MULTIPLE SOLUTIONS; EXISTENCE; PART; UNIQUENESS; CALCULUS;

D O I：

10.3934/cpaa.2018054

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we are concerned with the existence of ground state solutions for the following quasilinear Schrodinger equation: -Delta u + V(x)u -Delta(u(2))u=K(x)vertical bar u vertical bar(22*-2)u+g(x,u),x is an element of R-N (1) where N > 3, V, g are asymptotically periodic functions in x. By combining variational methods and the concentration-compactness principle, we obtain a ground state solution for equation (I) under a new reformative condition which unify the asymptotic processes of V, g at infinity.

引用

页码：1121 / 1145

页数：25

共 38 条

[31] Uniqueness and nondegeneracy of the ground state for a quasilinear Schrodinger equation with a small parameter [J].

Selvitella, Alessandro .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (05) :1731-1737

[32] Generalized quasilinear asymptotically periodic Schrodinger equations with critical growth [J].

Shi, Hongxia ;

Chen, Haibo .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2016, 71 (03) :849-858

[33] Quasilinear asymptotically periodic Schrodinger equations with critical growth [J].

Silva, Elves A. B. ;

Vieira, Gilberto F. .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2010, 39 (1-2) :1-33

[34] Quasilinear asymptotically periodic Schrodinger equations with subcritical growth [J].

Silva, Elves A. B. ;

Vieira, Gilberto F. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (06) :2935-2949

[35] Non-Nehari manifold method for asymptotically periodic Schrodinger equations [J].

Tang XianHua .

SCIENCE CHINA-MATHEMATICS, 2015, 58 (04) :715-728

[36] Multiple solutions for quasilinear Schrodinger equations with a parameter [J].

Wu, Xian .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 256 (07) :2619-2632

[37] Ground state solutions for asymptotically periodic Schrodinger equations with indefinite linear part [J].

Zhang, Hui ;

Xu, Junxiang ;

Zhang, Fubao .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2015, 38 (01) :113-122

[38] On a class of semilinear Schrodinger equations with indefinite linear part [J].

Zhang, Hui ;

Xu, Junxiang ;

Zhang, Fubao .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 414 (02) :710-724

← 1 2 3 4 →