Existence and convergence of ground state solutions for a (p, q) -Laplacian system on weighted graphs

We investigate the existence of ground state solutions for a (p, q) -Laplacian system with p, q>1 and potential wells on a weighted locally finite graph G= (V, E). By making use of the method of Nehari manifold and the Lagrange multiplier rule, we prove that if the nonlinear term F takes on the super- (p, q) -linear growth and the potential functions a (x) and b (x) satisfy some suitable conditions, then for any fixed parameter 1, the system is provided with a ground state solution (u_, v_). Additionally, we set up the convergence property of the solutions set \ (u_, v_) \ when +.