Multiple solutions for quasilinear elliptic problems with nonlinear boundary conditions

Chung, Nguyen Thanh

Electronic journal of differential equations, Tome 2008 (2008)

Résumé

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 $(1$ and $\mu$ are positive parameters.

Détail

Classification : 35J65, 35J20
Keywords: multiple solutions, quasilinear elliptic problems, nonlinear boundary conditions