Ground state solutions for diffusion system with superlinear nonlinearity

In this paper, we study the following diffusion system ( ¶ tu Dxu + b(t, x)r xu + V(x)u = g(t, x, v), ¶tv Dxv b(t, x)r xv + V(x)v = f(t, x, u) where z = (u, v) : R R N ! R 2 , b2 C 1 (R R N ,R N ) and V(x)2 C(R N ,R). Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin and Weth.