Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 165, pp. 1-6.
Title: Multiple solutions for quasilinear elliptic problems with
nonlinear boundary conditions
Author: Nguyen Thanh Chung (Quang Binh Univ., Vietnam)
Abstract:
Using a recent result by Bonanno [2], we obtain a
multiplicity result for the quasilinear elliptic problem
$$\displaylines{
- \Delta_p u + |u|^{p-2}u = \lambda f(u) \quad \hbox{in } \Omega, \cr
|\nabla u|^{p-2} \frac{\partial u}{\partial \nu}
= \mu g(u) \quad \hbox{on } \partial\Omega,
}$$
where $\Omega$ is a bounded domain in $\mathbb R^N$, $N \geq 3$
with smooth boundary $\partial\Omega$, $\frac{\partial}{\partial\nu}$
is the outer unit normal derivative,
the functions $f, g$ are $(p-1)$-sublinear at infinity
($1