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We investigate the existence of two nontrivial solutions for a poly-Laplaciansystem involving concave-convex nonlinearities and parameters with Dirichletboundary condition on locally finite graphs. By using the mountain pass theoremand Ekeland's variational principle, we obtain that system has at least onenontrivial solution of positive energy and one nontrivial solution of negativeenergy, respectively. We also obtain an estimate about semi-trivial solutions.Moreover, by using a result in [4] which is based on the fibering method andNehari manifold, we obtain the existence of ground state solution to the singleequation corresponding to poly-Laplacian system. Especially, we present someranges of parameters in all of results.

Existence of solutions for a poly-Laplacian system involving concave-convex nonlinearity on locally finite graphs