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

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.

Keywords

• group invariant solution
• least energy solution
• positive solution,variational method
• 35j20
• 35j25