Existence and convergence of solutions for p-Laplacian systems with homogeneous nonlinearities on graphs

In this paper, we investigate a class of p-Laplacian systems on locally finite graph $$G=(V,E)$$ . By exploiting the method Nehari manifold and some new analytical techniques, under suitable assumptions potentials nonlinear terms, prove that system admits ground state solution $$(u_{\lambda },v_{\lambda })$$ when parameter $$\lambda $$ is sufficiently large. Furthermore, consider concentration behavior these solutions as \rightarrow \infty , show converge to corresponding limit problem.