Infinitely many solutions for sublinear Kirchhoff equations in R^N with sign-changing potentials

Abstract

In this article we study the Kirchhoff equation $$ -Big(a+b int_{mathbb{R}^N}|abla u|^2dxBig)Delta u+V(x)u = K(x)|u|^{q-1}u, quadhbox{in }mathbb{R}^N, $$ where $Ngeq 3$, $00$ are constants and $K(x), V(x)$ both change sign in $mathbb{R}^N$. Under appropriate assumptions on V(x), K(x), the existence of infinitely many solutions is proved by using the symmetric Mountain Pass Theorem.

Keywords

• Kirchhoff equations
• symmetric Mountain Pass Theorem
• infinitely many solutions