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.