Boundary Value Problems for Fourth Order Nonlinearp-Laplacian Difference Equations

Abstract

We consider the boundary value problem for a fourth order nonlinearp-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.

Periodic and subharmonic solutions for a 2<inline-formula><tex-math id="M1">\begin{document}$n$\end{document}</tex-math></inline-formula>th-order <inline-formula><tex-math id="M2">\begin{document}$\phi_c$\end{document}</tex-math></inline-formula>-Laplacian difference equation containing both advances and retardations

“…In recent years, there has been much progress on the qualitative properties of difference equations and a lot of interesting results have been worked out, which included results on stability [5], attractivity [14], periodic solutions [3,6,7,8,9,11,17,18,27], homoclinic orbits [4,10,13,21,22,23,24,26,28], boundary value problems [19,20,25] and other topics [1,2,12].…”