Multiplicity of Nodal Solutions for a Class of $p$-Laplacian Equations in $\mathbb{R}^{N}$

Abstract

We consider a class of $p$-Laplacian equations in $\mathbb{R}^{N}$. By carefully analyzing the compactness of the Palais-Smale sequences and constructing Nehari manifolds, we prove that for every positive integer $m\geq 2$, there exists a nodal solution with at least $2m$ nodal domains.