Vol. 310, No. 1, 2021

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Multiple solutions for quasilinear elliptic equations with critical exponents in $\mathbb{R}^N$

Fengshuang Gao and Yuxia Guo

Vol. 310 (2021), No. 1, 49–83
Abstract

This paper is concerned with a class of quasilinear problems in N involving critical exponents, which includes the so called modified nonlinear Schrödinger equation (MNSE). By using the truncation method together with the regularization approach and the compactness arguments, we prove the existence of infinitely many solutions for the above mentioned problems.

Keywords
quasilinear equation, critical exponent, multiple solutions
Mathematical Subject Classification 2010
Primary: 35J91
Secondary: 35B33
Milestones
Received: 22 November 2018
Revised: 1 July 2020
Accepted: 5 December 2020
Published: 26 January 2021
Authors
Fengshuang Gao
Department of Mathematical Science
Tsinghua University
Beijing
China
Yuxia Guo
Department of Mathematical Science
Tsinghua University
Beijing
China