Existence Results for the p-Laplacian with Nonlinear Boundary Conditions

AbstractIn this paper we study the existence of nontrivial solutions for the problem Δpu=|u|p−2u in a bounded smooth domain Ω⊂RN, with a nonlinear boundary condition given by |∇u|p−2∂u/∂ν=f(u) on the boundary of the domain. The proofs are based on variational and topological arguments