Bull. Korean Math. Soc. 2016; 53(6): 1753-1769
Online first article September 22, 2016 Printed November 30, 2016
https://doi.org/10.4134/BKMS.b150923
Copyright © The Korean Mathematical Society.
Caisheng Chen and Qiang Chen
Hohai University, Yancheng Institute of Technology
This paper is concerned with the quasilinear Schr\"{o}dinger system \begin{equation}\label{0.1} \left\{ \begin{aligned} &-\Delta u+a(x)u-\Delta(u^2)u=F_u(u,v)+h(x) \quad \; x\in \mathbb{R}^N,\\ &-\Delta v+b(x)v-\Delta(v^2)v=F_v(u,v)+g(x) \quad \; x\in \mathbb{R}^N, \end{aligned} \right. \end{equation} where $ N \geq 3$. The potential functions $a(x), b(x)\in L^\infty(\mathbb{R}^N)$ are bounded in $\mathbb{R}^N$. By using mountain pass theorem and the Ekeland variational principle, we prove that there are at least two solutions to system (\ref{0.1}).
Keywords: quasilinear Schr\"{o}dinger system, mountain pass theorem, Ekeland's variational principle
MSC numbers: 35J20, 35J70, 35J91
2017; 54(1): 125-144
2017; 54(3): 715-729
2016; 53(5): 1585-1596
2012; 49(4): 737-748
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd