ON EXISTENCE OF NONTRIVIAL SOLUTIONS OF NEUMANN BOUNDARY VALUE PROBLEMS FOR QUASI-LINEAR ELLIPTIC EQUATIONS

Abstract

In the present paper, some new existence results of nontrivial solutions are obtained for the following Neumann boundary value problem involving the p-Laplacian

\triangle_p (u) = f(x, u) in \Ome

\frac{\partial u}{\partial n}=0, in \partial \Omega

and conditions in recent literature for guaranteeing the existence of solutions with saddle point character are improved.