POSITIVE SOLUTIONS OF THE p-LAPLACE EMDEN-FOWLER EQUATION IN HOLLOW THIN SYMMETRIC DOMAINS

We study the existence of positive solutions for the p-Laplace Emden-Fowler equation. Let H and G be closed subgroups of the orthogonal group O(N) such that H not subset of G subset of O(N). We denote the orbit of G through x is an element of R-N by G (x), i.e., G(x) := {gx : g is an element of G}. We prove that if H(x) not subset of G(x) for all x is an element of Omega and the first eigenvalue of the p-Laplacian is large enough, then no H invariant least energy solution is G invariant. Here an H invariant least energy solution means a solution which achieves the minimum of the Rayleigh quotient among all H invariant functions. Therefore there exists an H invariant G non-invariant positive solution.