Existence results for quasilinear Schrödinger equations under a general critical growth term

Yan-Fang Xue, Jian-Xin Han, Xin-cai Zhu Annales Polonici Mathematici MSC: 35J60, 35J62, 35B09. DOI: 10.4064/ap200709-11-1 Published online: 6 April 2021

Abstract

We study the existence of solutions for the following quasilinear Schrödinger equation: $$ -\Delta u-\Delta (u^2)u=|u|^{2\cdot 2^*-2}u+g(u), \quad x\in \mathbb {R}^N, $$ where $N\geq 3$ and $g$ satisfies very weak growth conditions. The method is to analyze the behavior of solutions for subcritical problems from Colin and Jeanjean’s work [Nonlinear Anal. 56 (2004), 213–226] and to take the limit as the exponent approaches the critical exponent.

Authors

  • Yan-Fang XueSchool of Mathematics and Statistics
    Xinyang Normal University
    464000 Henan, China
    e-mail
  • Jian-Xin HanSchool of Mathematics and Statistics
    Xinyang Normal University
    464000 Henan, China
    e-mail
  • Xin-cai ZhuSchool of Mathematics and Statistics
    Xinyang Normal University
    464000 Henan, China
    e-mail

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