Existence of ground state solutions for critical quasilinear Schrödinger equations with steep potential well-Reference-Cited by-同舟云学术

Existence of ground state solutions for critical quasilinear Schrödinger equations with steep potential well

Published:2022-01-01 Issue:1 Volume:22 Page:619-634
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Xue Yan-Fang¹,Zhong Xiao-Jing²,Tang Chun-Lei³

Affiliation:

1. School of Mathematics and Statistics, Xin-Yang Normal University , Xinyang , Henan 464000 , People’s Republic of China

2. School of History, Culture and Ethnology, Southwest University , Chongqing 400715 , People’s Republic of China

3. School of Mathematics and Statistics, Southwest University , Chongqing 400715 , People’s Republic of China

Abstract

Abstract We study the existence of solutions for the quasilinear Schrödinger equation with the critical exponent and steep potential well. By using a change of variables, the quasilinear equations are reduced to a semilinear one, whose associated functionals satisfy the geometric conditions of the Mountain Pass Theorem for suitable assumptions. The existence of a ground state solution is obtained, and its concentration behavior is also considered.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2022-0030/pdf

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