Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 90, pp. 1-14.
Title: Infinitely many weak solutions for a $p$-Laplacian equation
with nonlinear boundary conditions
Authors: Ji-Hong Zhao (Lanzhou Univ., Lanzhou, China)
Pei-Hao Zhao (Lanzhou Univ., Lanzhou, China)
Abstract:
We study the following quasilinear problem with
nonlinear boundary conditions
$$\displaylines
-\Delta _{p}u+a(x)|u|^{p-2} u=f(x,u) \quad \mbox{in }\Omega, \cr
|\nabla u|^{p-2} \frac{\partial u}{\partial \nu}=g(x,u) \quad
\mbox{on } \partial\Omega,
}$$
where $\Omega$ is a bounded domain in $\mathbb{R}^{N}$ with smooth
boundary and $\frac{\partial}{\partial \nu}$ is the outer normal
derivative, $\Delta_{p}u=\mathop{\rm div}(|\nabla u|^{p-2}\nabla u)$ is the
$p$-Laplacian with $1