Infinitely many sign-changing solutions for Kirchhoff-type equations with power nonlinearity

• Main Authors: Xianzhong Yao, Chunlai Mu
• Format: Article
• Language: English
• Published: Texas State University 2016-02-01
• Series: Electronic Journal of Differential Equations
• Subjects: Kirchhoff-type; sign-changing solutions; invariant sets of descent flow
• Online Access: http://ejde.math.txstate.edu/Volumes/2016/59/abstr.html

In this article we consider the Kirchhoff-type elliptic problem $$\displaylines{ -(a+b\int_{\Omega}|\nabla u|^2dx)\Delta u=|u|^{p-2}u, \quad\text{in } \Omega,\cr u=0, \quad \text{on } \partial\Omega, }$$ where $\Omega\subset\mathbb{R}^N$ and $p\in(2,2^*)$ with $2^*=\frac{2N}{N-2}$ if $N\geq 3$, and $2^*=+\infty$ otherwise. We show that the problem possesses infinitely many sign-changing solutions by using combination of invariant sets of descent flow and the Ljusternik-Schnirelman type minimax method.