A model of capillary phenomena in $\mathbb R^N$ with subcritical growth
Calogero Vetro · Rendiconti Lincei Matematica e Applicazioni · 2020
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.