Solutions of Schrödinger equations with inverse square potential and critical nonlinearity

In this paper, we are concerned with the following nonlinear Schrödinger equations with inverse square potential and critical Sobolev exponent(P)−Δu−μu|x|2+a(x)u=|u|2⁎−2u+f(x,u),u∈H1(RN), where 2⁎=2N/(N−2) is the critical Sobolev exponent, 0⩽μ

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Bibliographic Details
Published in:Journal of Differential Equations 2012-09, Vol.253 (5), p.1376-1398
Main Authors: Deng, Yinbin, Jin, Lingyu, Peng, Shuangjie
Format: Article
Language:English
Subjects:
Compactness
Critical Sobolev exponent
Nonlinear Schrödinger equation
Palais–Smale sequence
Positive solutions
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Summary:In this paper, we are concerned with the following nonlinear Schrödinger equations with inverse square potential and critical Sobolev exponent(P)−Δu−μu|x|2+a(x)u=|u|2⁎−2u+f(x,u),u∈H1(RN), where 2⁎=2N/(N−2) is the critical Sobolev exponent, 0⩽μ
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2012.05.009