Multiple Nontrivial Solutions for a Class of p-Laplacian Equations

In this paper a class of p-Laplacian equations are considered. The existence of five nontrivial solutions is stated. By the standard supersolution and subsolution method, we prove the existence of minimal positive solution and maximal negative solution in L ^∞(Ω). Furthermore, in virtue of the well-known Mountain-Pass Theorem and Second Deformation Theorem, we can give additional three nontrivial solutions, i.e., one positive solution, one negative solution and one sign-changing solution.