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

Date

2020-05-27

Authors

Wang, Xiaohui
Zhao, Peihao

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

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.

Description

Keywords

Superlinear elliptic system, Weak solution, Mountain pass lemma, Linking theorem

Citation

Wang, X., & Zhao, P. (2020). Existence of weak solutions to superlinear elliptic systems without the Ambrosetti-Rabinowitz condition. <i>Electronic Journal of Differential Equations, 2020</i>(52), pp. 1-21.

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Attribution 4.0 International

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