Abstract
We study the following coupled elliptic
system with critical nonlinearities:
\left\{\begin{aligned} &\displaystyle-\triangle{u}+u=f(u)+\beta h(u)K(v),&&%
\displaystyle x\in{\mathbb{R}}^{N},\\
&\displaystyle-\triangle{v}+v=g(v)+\beta H(u)k(v),&&\displaystyle x\in{\mathbb%
{R}}^{N},\\
&\displaystyle u,v\in H^{1}({\mathbb{R}}^{N}),\end{aligned}\right.
where
{\beta>0}
; f, g are differentiable functions with critical
growth; and
{H,K}
are primitive functions of h and k,
respectively. Under some assumptions on f, g, h and k, we
obtain the existence of a positive ground state solution of this
system for
{N\geq 2}
.
Ground state solution of a noncooperative elliptic system
