Existence of ground state solution of Nehari-Pohožaev type for a quasilinear Schrödinger system

This paper is concerned with the following quasilinear Schrödinger system in the entire space ${\mathbb{R}}^N$($N\ge 3$): $$\{\begin{array}{rllll}& {\displaystyle }& {\displaystyle -\mathrm{\Delta }u+A(x)u-\frac{1}{2}\mathrm{△}(u^2)u=\frac{2\alpha }{\alpha +\beta }\mathrm{\mid }u{\mathrm{\mid }}^{\alpha -2}u\mathrm{\mid }v{\mathrm{\mid }}^{\beta },}& & \\ & {\displaystyle }& {\displaystyle -\mathrm{\Delta }v+Bv-\frac{1}{2}\mathrm{△}(v^2)v=\frac{2\beta }{\alpha +\beta }\mathrm{\mid }u{\mathrm{\mid }}^{\alpha }\mathrm{\mid }v{\mathrm{\mid }}^{\beta -2}v\mathrm{.}}& & \end{array}$$ 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).