Existence of a ground-state solution for a quasilinear Schrödinger system

In this paper, we consider the following quasilinear Schr & ouml;dinger system. {-Delta u+u+k/2 Delta|u|(2)[]u=2 alpha/alpha+beta|(u|alpha)-(2)u|v|(beta), x is an element of R-N, -Delta v+v+k/2 Delta|v|2[]v2 beta/alpha+beta|u|alpha|v|(beta)-2v,x is an element of R-N, where k<0 is a real constant, alpha>1,beta>1, and alpha+beta<2*. We take advantage of the critical point theorem developed by Jeanjean (Proc. R. Soc. Edinburgh Sect A.,1999, 129: 787-809) and combine it with Poho & zcaron;aev identity to obtain the existence of a ground-state solution, which is the non-trivial solution with the least possible energy.