Multiplicity of solutions for a p-Laplacian equation with nonlinear boundary conditions

Document Type : Research Paper


Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran


In this paper we use the three critical points theorem attributed to B. Ricceri in order to establish existence of three distinct solutions for the following boundary value problem:

\left\{ \begin{array}{ll} \Delta_p u = a(x) |u|^{p-2} u & \mbox{ in
$\Omega$,}\\\\ |\nabla u|^{p-2} \nabla u . \nu = \lambda f(x,u)
& \mbox{ on $\partial\Omega$.}\end{array} \right.