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AbstractThis paper derives several sufficient conditions for the existence of three solutions to the Dirichlet problem for a second-order self-adjoint difference equation involving p-Laplacian through the critical point theory. Furthermore, by using the strong maximum principle, we prove that the three solutions are positive under appropriate assumptions on the nonlinearity. Finally, we present three examples to confirm our results.doi:10.1186/s13662-021-03350-8 fatcat:2symlhjkijhkjddiocxfwoy3dm