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

نویسندگان

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

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

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چکیده

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: \begin{eqnarray*} \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. \end{eqnarray*}