Existence of Nontrivial Solutions for p-Laplacian Equations in {R}^{N}

Abstract

In this paper, we consider a p-Laplacian equation in {R}^{N}with sign-changing potential and subcritical p-superlinear nonlinearity. By using the cohomological linking method for cones developed by Degiovanni and Lancelotti in 2007, an existence result is obtained. We also give a result on the existence of periodic solutions for one-dimensional $p$-Laplacian equations which can be proved by the same method.