Weak solutions for the p-Laplacian with a nonlinear boundary condition at resonance

Abstract

We study the existence of weak solutions to the equation Δpu = |u|p-2u + ƒ(x, u) with the nonlinear boundary condition |∇u|p-2 ∂u/ ∂v = λ|u|p-2 u-h(x, u). We assume Landesman-Lazer type conditions and use variational arguments to prove the existence of solutions.