  In this paper, we study the existence of a ground state solution, that is, a
non trivial solution with least energy, of a noncooperative semilinear elliptic
system on a bounded domain. By using the method of the generalized Nehari
manifold developed recently by Szulkin and Weth, we prove the existence of a
ground state solution when the nonlinearity is subcritical and satisfies a weak
superquadratic condition.
