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

DOI: 10.2140/pjm.2021.310.49

Abstract

This paper is concerned with a class of quasilinear problems in ${ℝ}^N$ 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