Existence of weak solutions to superlinear elliptic systems without the Ambrosetti-Rabinowitz condition

Abstract

In this article, we study the existence of the weak solution for superlinear elliptic equations and systems without the Ambrosetti-Rabinowitz condition. The Ambrosetti-Rabinowitz condition guarantees the boundedness of the PS sequence of the functional I for the corresponding problem. We establish the existence of the weak solution for the superlinear elliptic equation by using (PS)c form of the Mountain pass lemma, and the existence of the weak solution for the superlinear elliptic system by using (PS)*c form of the Linking theorem.