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.


Volume 7, Issue 3
July 2019
Pages 475-479
  • Receive Date: 14 March 2018
  • Revise Date: 25 July 2018
  • Accept Date: 08 September 2018
  • First Publish Date: 01 July 2019