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Multiplicity of Nodal Solutions for a Class of p-Laplacian Equations in RN

Commun. Math. Anal.
Volume 12, Number 2 (2012), 120 - 136

Multiplicity of Nodal Solutions for a Class of p-Laplacian Equations in RN

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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.