Quasilinear Problems Involving Changing-Sign Nonlinearities Without an Ambrosetti-Rabinowitz-Type Condition

In this paper quasilinear elliptic boundary value equations without an Ambrosetti and Rabinowitz growth condition are considered. Existence of a non-trivial solution result is established. For this, we show the existence of a Cerami sequence by using a variant of the mountain-pass theorem due to Schechter. The novelty here is that we may consider nonlinearities that satisfy a local p-superlinear condition and may change sign. Copyright © 2014 Edinburgh Mathematical Society.