On the existence of three solutions for quasilinear elliptic problem

Abstract

We consider a quasilinear elliptic problem of the type \(-\Delta_p u = \lambda (f(u)+\mu g(u))\) in \(\Omega\), \(u|_{\partial \Omega} =0\), where \(\Omega \in \mathbb{R}^N\) is an open and bounded set, \(f\), \(g\) are continuous real functions on \(\mathbb{R}\) and \(\lambda , \mu \in \mathbb{R}\). We prove the existence of at least three solutions for this problem using the so called three critical points theorem due to Ricceri.

Keywords

• critical point
• elliptic problem
• minimax inequality
• \(p\)-Laplacian
• three critical points theorem
• weak solution