Solutions of Schrodinger equations with inverse square potential and critical nonlinearity

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:253

Article

Deng, Yinbin¹  Jin, Lingyu²  Peng, Shuangjie¹ 

[1] Huazhong Normal Univ, Dept Math, Wuhan 430079, Peoples R China

[2] S China Agr Univ, Coll Sci, Guangzhou 510642, Guangdong, Peoples R China

关键词: Compactness;    Critical Sobolev exponent;    Nonlinear Schrodinger equation;    Positive solutions;    Palais-Smale sequence;   

DOI  :  10.1016/j.jde.2012.05.009

来源: Elsevier

【 摘 要 】

In this paper, we are concerned with the following nonlinear Schrodinger equations with inverse square potential and critical Sobolev exponent -Delta u - mu u/vertical bar x vertical bar(2) + a(x)u = vertical bar u vertical bar(2)*(-2)u + f(x, u), u is an element of H-1(R-N), (P) where 2* = 2N/(N - 2) is the critical Sobolev exponent, 0 <= mu < <(mu)over bar> := (N-2)(2)/4, a(x) is an element of C(R-N). We first give a representation to the Palais-Smale sequence related to (P) and then obtain an existence result of positive solutions of (P). Our assumptions on a(x) and f(x, u) are weaker than the known cases even if mu = 0. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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