Multiple solutions for a class of quasilinear Schr\"{o}dinger system in $\mathbb{R}^N$
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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}).
Abstract
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}).
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