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