Ground State Solutions for Kirchhoff Equations via Modified Nehari-Pankov Manifold

Abstract

We investigate the Kirchhoff type elliptic problem $$\Bigg(a+b\int_{\mathbb{R}^N}[|\nabla u|^2+V(x)u^2]dx\Bigg)[-\Delta u+V(x)u]=f(x,u), \ \ \ x\in \mathbb{R}^N,$$where both $V$ and $f$ are periodic in $x,$ 0 belongs to a spectral gap of $−∆+V.$ Under suitable assumptions on $V$ and $f$ with more general conditions, we prove the existence of ground state solutions and infinitely many geometrically distinct solutions.