Multiplicity results for p(x)-biharmonic equations with Navier boundary conditions

Abstract

This paper deals with the existence of solutions for a class of p(x)-biharmonic equations with Navier boundary conditions. The approach is based on variational methods and critical point theory. Indeed, we investigate the existence of two solutions for the problem under some algebraic conditions with the classical Ambrosetti–Rabinowitz condition on the nonlinear term. Moreover, by combining two algebraic conditions on the nonlinear term which guarantee the existence of two solutions, applying the mountain pass theorem given by Pucci and Serrin we establish the existence of the third solution for the problem.