Ground state solutions for Kirchhoff-type equations with a general nonlinearity in the critical growth

Advances in Nonlinear Analysis

article

Li-Ping Xu¹  Haibo Chen² 

[1] Department of Mathematics and Statistics, Henan University of Science and Technology;School of Mathematics and Statistics, Central South University

关键词: Kirchhoff-type equations;    critical growth;    ground state solutions;    variational methods;   

DOI  :  10.1515/anona-2016-0073

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

In this paper, we concern ourselves with the following Kirchhoff-type equations: {-(a+b⁢∫ℝ3|∇⁡u|2⁢?x)⁢△⁢u+V⁢u=f⁢(u) in ⁢ℝ3,u∈H1⁢(ℝ3),\left\{\begin{aligned} \displaystyle-\biggl{(}a+b\int_{\mathbb{R}^{3}}\lvert% \nabla u\rvert^{2}\,dx\biggr{)}\triangle u+Vu&\displaystyle=f(u)\quad\text{in % }\mathbb{R}^{3},\\ \displaystyle u&\displaystyle\in H^{1}(\mathbb{R}^{3}),\end{aligned}\right. where a , b and V are positive constants and f has critical growth. We use variational methods to prove the existence of ground state solutions. In particular, we do not use the classical Ambrosetti–Rabinowitz condition. Some recent results are extended.

【 授权许可】

CC BY