On ground states for the Kirchhoff-type problem with a general critical nonlinearity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:426

Article

Liu, Zhisu¹  Guo, Shangjiang¹ 

[1] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China

关键词: Kirchhoff type problem;    Critical nonlinearity;    Ground state;    Variational methods;   

DOI  :  10.1016/j.jmaa.2015.01.044

来源: Elsevier

【 摘 要 】

In this paper, we consider the following Kirchhoff-type problem {-(a + b integral(R3) vertical bar del u vertical bar(2)) Delta u = f(u), in R-3, u is an element of H-1 (R-3), u > 0, in R-3, where a, b > 0 are constants, and f has a critical growth. The aim of this paper is to study the existence of ground state solutions for Kirchhoff-type equations with a general nonlinearity in the critical growth, without the assumption of the monotonicity of the function t -> f(t)/t(3). Moreover, we will show that the mountain pass value gives the least energy level and also obtain a mountain pass solution. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free