Multiple solutions for a Kirchhoff-type equation with general nonlinearity

Advances in Nonlinear Analysis

article

Sheng-Sen Lu¹ 

[1] Center for Applied Mathematics, Tianjin University;Chern Institute of Mathematics and LPMC, Nankai University

关键词: Kirchhoff-type equation;    Berestycki–Lions-type nonlinearity;    multiplicity results;    variational methods;   

DOI  :  10.1515/anona-2016-0093

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

This paper is devoted to the study of the following autonomous Kirchhoff-type equation: -M⁢(∫ℝN|∇⁡u|2)⁢Δ⁢u=f⁢(u),u∈H1⁢(ℝN),-M\biggl{(}\int_{\mathbb{R}^{N}}|\nabla{u}|^{2}\biggr{)}\Delta{u}=f(u),\quad u% \in H^{1}(\mathbb{R}^{N}), where M is a continuous non-degenerate function and N≥2{N\geq 2}. Under suitable additional conditions on M and general Berestycki–Lions-type assumptions on the nonlinearity of f , we establish several existence results of multiple solutions by variational methods, which are also naturally interpreted from a non-variational point of view.

【 授权许可】

CC BY