Concentration of positive solutions for critical quasilinear Schrödinger equation with competing potentials. Issue 9 (4th July 2021)

• Record Type: Journal Article
• Authors: Chen, Yongpeng
• Is Part Of: Applicable analysis. Volume 100:Issue 9(2021)
• Page Start: 1925
• Page End: 1948
• Publication Date: 2021-07-04
• Subjects: Quasilinear Schrödinger equation -- critical exponent -- concentration -- competing potential; 35Q55 -- 35J65; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1671975
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we study a class of singularly perturbed critical quasilinear Schrödinger equation of the form 1 − ε 2 Δ u + V ( x ) u − ε 2 ( Δ u 2 ) u = P ( x ) | u | p − 2 u + Q ( x ) | u | 2 ⋅ 2 ∗ − 2 u, in R N . By using a change of variables and variational argument, we prove the existence of positive solutions and their concentration behavior.