Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 37, pp. 1-7.

Title: Multiple solutions for the $p$-Laplace equation with nonlinear
       boundary conditions
       
Author: Julian Fernandez Bonder (Univ. Buenos Aires, Argentina)

Abstract: 
 In this note, we show the existence of at least three nontrivial
 solutions to the  quasilinear elliptic equation
 $$
 -\Delta_p u + |u|^{p-2}u = f(x,u)
 $$
 in a smooth bounded domain $\Omega$ of $\mathbb{R}^N$
 with nonlinear boundary conditions
 $|\nabla u|^{p-2}\frac{\partial u}{\partial\nu} = g(x,u)$
 on $\partial\Omega$. The proof is based on variational arguments.
 
Submitted January 10, 2006. Published March 21, 2006.
Math Subject Classifications: 35J65, 35J20.
Key Words: $p$-Laplace equations; nonlinear boundary conditions;
           variational methods.