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.

Keywords

• superlinear elliptic system
• weak solution
• mountain pass lemma
• linking theorem