We consider the boundary value problem for a fourth order nonlinear p-Laplacian difference equation containing both advance and retardation. By using Mountain pass lemma and some established inequalities, sufficient conditions of the existence of solutions of the boundary value problem are obtained. And an illustrative example is given in the last part of the paper.
"Boundary Value Problems for Fourth Order Nonlinear -Laplacian Difference Equations." J. Appl. Math. 2014 1 - 6, 2014. https://doi.org/10.1155/2014/343129