Weak solution for Neumann (p,q)-Laplacian problem on Riemannian manifold

Abstract

We prove the existence of a nontrivial solution for a nonlinear (p,q)-Laplacian problem with Neumann boundary condition, on a non compact Riemannian manifold. The idea is to reduce the problem in variational form, which means to consider the critical points of the corresponding Euler-Lagrange functional in an Orlicz-Sobolev space.