Infinitely Many Weak Solutions of the p-Laplacian Equation with Nonlinear Boundary Conditions

Abstract

We study the following p-Laplacian equation with nonlinear boundary conditions: -Δpu+μ(x)|u|p-2u=f(x,u)+g(x,u), x∈Ω,|∇u|p-2∂u/∂n=η|u|p-2u and x∈∂Ω, where Ω is a bounded domain in ℝN with smooth boundary ∂Ω. We prove that the equation has infinitely many weak solutions by using the variant fountain theorem due to Zou (2001) and f,g do not need to satisfy the (P.S) or (P.S*) condition.