Singular perturbed Kirchhoff type problem with critical exponent

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:454

Article

Xie, Qilin¹ 

[1] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Guangdong, Peoples R China

关键词: Kirchhoff type problem;    Critical exponent;    Concentration behavior;   

DOI  :  10.1016/j.jmaa.2017.04.048

来源: Elsevier

【 摘 要 】

In the present paper, we consider the following Kirchhoff type problem with critical exponent (-(epsilon(2)a + epsilon b integral(R3)vertical bar del u vertical bar(2)dx)Delta u + V(x)u = f(u), in R-3 u is an element of H-1(R-3). By variational methods, we show the existence of the positive solutions concentrating around global minima of the potential V(x), as epsilon -> 0. We do not need the monotonicity of the function xi -> f(xi)/xi(3). (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free