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2021 Multiplicity and concentration results for a class of singularly perturbed critical quasilinear Schrödinger equation
Yongpeng Chen, Zhongwei Tang
Topol. Methods Nonlinear Anal. 57(1): 135-171 (2021). DOI: 10.12775/TMNA.2019.115

Abstract

In this paper, we study a class of singularly perturbed critical quasilinear Schrödinger equation of the form $$ -\varepsilon^2\Delta u+V(x)u-\varepsilon^2(\Delta u^2)u=P(x)|u|^{p-2}u+Q(x)|u|^{2\cdot2^*-2}u,\quad \hbox{in } \mathbb{R}^N. $$ By using a change of variables and variational argument, we prove not only the existence of positive ground state solutions and their concentration behavior, but also the existence and associated concentration behavior of multiple solutions.

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Yongpeng Chen. Zhongwei Tang. "Multiplicity and concentration results for a class of singularly perturbed critical quasilinear Schrödinger equation." Topol. Methods Nonlinear Anal. 57 (1) 135 - 171, 2021. https://doi.org/10.12775/TMNA.2019.115

Information

Published: 2021
First available in Project Euclid: 10 September 2020

Digital Object Identifier: 10.12775/TMNA.2019.115

Rights: Copyright © 2020 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.57 • No. 1 • 2021
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