Existence and multiplicity of solutions for nonlinear 2n-th order difference boundary value problems

We prove existence and multiplicity results for a general 2n-th order discrete boundary value problem. We exploit the finite dimension of function spaces and some simple results from matrix theory to construct a nonlinear equation in RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^{N}$$\end{document} which is eventually studied with the fixed point theory, degree theory and variational methods.