Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 52, pp. 1-21.

Title: Existence of weak solutions to superlinear elliptic systems without
       the Ambrosetti-Rabinowitz condition
       
Authors: Xiaohui Wang (Lanzhou Univ., Lanzhou, China)
         Peihao Zhao  (Lanzhou Univ., Lanzhou, China)

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.
 
Submitted May 8, 2018. Published May 27, 2020.
Math Subject Classifications: 35J20, 35J47, 35J15, 35A15.
Key Words: Superlinear elliptic system; weak solution;
           mountain pass lemma; linking theorem.