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).

中文翻译：

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拟线性薛定ding系统的Nehari-Pohožaev型基态解的存在性

本文涉及整个空间$ \ mathbb R ^ {N} $（$ N \ geq3 $）中的以下拟线性Schrödinger系统：$$ \ begin {cases}-\ Delta u + A（x）u- \ frac {1} {2} \ triangle（u ^ {2}）u = \ frac {2 \ alpha} {\ alpha + \ beta} | u | ^ {\ alpha-2} u | v | ^ {\ beta} ，\\-\ Delta v + Bv- \ frac {1} {2} \ triangle（v ^ {2}）v = \ frac {2 \ beta} {\ alpha + \ beta} | u | ^ {\ alpha} | v | ^ {\ beta-2} v。\ end {cases} $$通过建立合适的约束集并研究相关的最小化问题，我们证明了$ \ alpha，\ beta> 1 $，$ 2 <\ alpha + \ beta <\ frac {4N}的基态解的存在{N-2} $。我们的结果可以看做是对Guo和Tang（准线性Schrödinger系统的地面状态解，J。Math。Anal。Appl。389（2012）322）的概括。