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January/February 2021 Existence of ground state solution of Nehari-Pohožaev type for a quasilinear Schrödinger system
Jianqing Chen, Qian Zhang
Differential Integral Equations 34(1/2): 1-20 (January/February 2021).

Abstract

This paper is concerned with the following quasilinear Schrödinger system in the entire space $\mathbb R^{N}$($N\geq3$): $$ \begin{cases} -\Delta u+A(x)u-\frac{1}{2} \triangle(u^{2})u=\frac{2\alpha}{\alpha+\beta} |u|^{\alpha-2}u|v|^{\beta},\\ -\Delta v+Bv-\frac{1}{2}\triangle(v^{2}) v=\frac{2\beta}{\alpha+\beta}|u|^{\alpha} |v|^{\beta-2}v. \end{cases} $$ By establishing a suitable constraint set and studying related minimization problem, we prove the existence of ground state solution for $\alpha,\beta > 1$, $2 < \alpha+\beta < \frac{4N}{N-2}$. Our results can be looked on as a generalization to results by Guo and Tang (Ground state solutions for quasilinear Schrödinger systems, J. Math. Anal. Appl. 389 (2012) 322).

Citation

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Jianqing Chen. Qian Zhang. "Existence of ground state solution of Nehari-Pohožaev type for a quasilinear Schrödinger system." Differential Integral Equations 34 (1/2) 1 - 20, January/February 2021.

Information

Published: January/February 2021
First available in Project Euclid: 12 January 2021

MathSciNet: MR4198539

Subjects:
Primary: 35J20 , 35J60

Rights: Copyright © 2021 Khayyam Publishing, Inc.

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Vol.34 • No. 1/2 • January/February 2021
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