Existence of infinitely many solutions of p-Laplacian equations in R^N+

Abstract

In this article, we study the p-Laplacian equation -∆pu = 0, in ℝN+, |∇u|p-2 ∂u/∂n + α(y)|u|p-2u = |u|q-2u, on ∂ℝN+ = ℝN-1, where 1 < p < N, p < q < p̄ = (N - 1)p/ N - p, ∆p = div(|∇u|p-2∇u) the p-Laplacian operator, and the positive, finite function α(y) satisfies suitable decay assumptions at infinity. By using the truncation method, we prove the existence of infinitely many solutions.