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

Abstract EN

We study the following p -Laplacian equation with nonlinear boundary conditions: - Δ p u + μ ( x ) | u | p - 2 u = f ( x , u ) + g ( x , u ) , x ∈ Ω , | ∇ u | p - 2 ∂ u / ∂ n = η | u | p - 2 u and x ∈ ∂ Ω , where Ω is a bounded domain in ℝ N 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.