On the existence of three solutions for quasilinear elliptic problem

Paweł Goncerz

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.

Mathematics Subject Classification: 35J20, 35J25, 35J92, 58E05.

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