Sign-changing and nontrivial solutions for a class of Kirchhoff-type problems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:481

Article

Chen, Bin¹  Ou, Zeng-Qi¹ 

[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

关键词: Kirchhoff-type equation;    Sign-changing solution;    Nehari manifold;    Nontrivial solution;    Deformation Lemma;   

DOI  :  10.1016/j.jmaa.2019.123476

来源: Elsevier

【 摘 要 】

In this paper, we study the existence of sign-changing (nodal) and nontrivial solutions for the nonlinear Kirchhoff-type equation {-(a+b integral(Omega)vertical bar del u vertical bar(2)dx) Delta u = alpha u + beta u(3) in Omega, u=0 on partial derivative Omega, where alpha, beta is an element of R are two real parameters. With the help of nodal Nehari set, we first provide a description of a two-dimensional set in the (alpha,beta) plane, which corresponds to the nonexistence and existence of sign-changing solutions for the above Kirchhoff type equation. And then, we establish the existence result of nontrivial solutions via the minimax methods. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free