We consider a kind of nonlinear systems on a locally finite graphs G = (V, E). We prove via the mountain pass theorem that this kind of systems has a nontrivial ground state solution which depends on the parameter λ with some suitable assumptions on the potentials. Moreover, we pay attention to the concentration behavior of these solutions and prove that, as λ → ∞, these solutions converge to a ground state solution of a corresponding Dirichlet problem. Finally, we also provide some numerical experiments to illustrate our results.

No abstract