Symmetric and Asymmetric Solutions of p-Laplace Elliptic Equations in Hollow Domains

Abstract

Abstract In the present paper, we study the p-Laplace equation in a hollow symmetric bounded domain. Let H and G be closed subgroups of the orthogonal group such that H ⊊ G {H\varsubsetneq G} . Then we prove the existence of a positive solution which is H-invariant and G-non-invariant. Furthermore, we give several examples of H, G and Ω, and find symmetric and asymmetric solutions.