Periodic and subharmonic solutions for a 2n2nth-order difference equation involving pp-Laplacian

By using the critical point theory, some new criteria are obtained for the existence and multiplicity of periodic and subharmonic solutions to a 2nnth-order nonlinear difference equation containing both advance and retardation involving pp-Laplacian. The proof is based on the Linking Theorem in combination with variational technique. Our results generalize and improve the results in the literature.