Ground state solutions for diffusion system with superlinear nonlinearity

摘要

In this paper, we study the following diffusion system egin{equation*} egin{cases} partial_{t}u-Delta_{x} u +b(t,x)cdot abla_{x} u +V(x)u=g(t,x,v), -partial_{t}v-Delta_{x} v -b(t,x)cdot abla_{x} v +V(x)v=f(t,x,u) end{cases} end{equation*} where $z=(u,v)colonmathbb{R}imesmathbb{R}^{N}ightarrowmathbb{R}^{2}$, $bin C^{1}(mathbb{R}imesmathbb{R}^{N}, mathbb{R}^{N})$ and $V(x)in C(mathbb{R}^{N},mathbb{R})$. 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.