The existence and nonexistence results of ground state nodal solutions for a Kirchhoff type problem

Abstract

In this paper, we investigate the existence and nonexistence of ground state nodal solutions to a class of Kirchhoff type problems \begin{document} $ -\left( a+b\int_{\Omega }{|}\nabla u{{|}.{2}}dx \right)\vartriangle u=\lambda u+|u{{|}.{2}}u, u\in H_{0}.{1}(\Omega ), $ \end{document} where $a, b>0$, $\lambda 0$ such that the Kirchhoff type problem possesses at least one ground state nodal solution $u_b$ for all $0 21 ], X.H. Tang and B.T. Cheng (2016)[ 22 ].