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

In this article, we study the p-Laplacian equation $$\displaylines{ -\Delta_p u=0, \quad \text{in } \mathbb{R}^N_{+},\cr |\nabla u|^{p-2}\frac{\partial u}{\partial n}+a(y)|u|^{p-2}u=|u|^{q-2}u , \quad \text{on } \partial\mathbb{R}^N_{+}=\mathbb{R}^{N-1}, }$$ where $1