A model of capillary phenomena in ${\mathbb{R}}^N$ with subcritical growth

Abstract

This paper deals with the nonlinear Dirichlet problem of capillary phenomena involving an equation driven by the $p$-Laplacian-like di¤erential operator in ${\mathbb{R}}^N$. We prove the existence of at least one nontrivial nonnegative weak solution, when the reaction term satisfies a sub-critical growth condition and the potential term has certain regularities. We apply the energy functional method and weaker compactness conditions.