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

Abstract

This paper is concerned with the following quasilinear Schrödinger system in the entire space $\mathbb R^{N}$($N\geq3$): $$\left\{\begin{align} &-Δu+A(x)u-\frac{1}{2}\triangle(u^{2})u = \frac{2α}{α+β}|u|^{α-2}u|v|^β,\\ &-Δv+Bv-\frac{1}{2}\triangle(v^{2})v=\frac{2β}{α+β}|u|^α|v|^{β-2}v.\end{align}\right. $$ By establishing a suitable constraint set and studying related minimization problem, we prove the existence of ground state solution for $α,β>1$, $2<α+β<\frac{4N}{N-2}$. 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).