Three Solutions for a Class of (p1, ..., pn)-Biharmonic Systems via Variational Methods

Shapour Heidarkhani

Abstract

In this paper, we prove the existence of at least three weak solutions to a boundary value problem for a system of n coupled equations involving (p1, ..., pn)-biharmonic Laplacians. We use a variational approach based on a three critical points theorem due to Ricceri [B. Ricceri, A three critical points theorem revisited, Nonlinear Anal. 70 (2009) 3084–3089].