Based on the fixed-point theorem in a cone and some analysis skill, a new sufficient condition is obtained for the existence of positive periodic solutions for a class of higher-order functional difference equations. An example is used to illustrate the applicability of the main result.
The existence of solutions for boundary value problems for a nonlinear discrete system involving the -Laplacian is investigated. The approach is based on critical point theory.
In this paper we establish the existence of single and multiple solutions to the positone discrete Dirichlet boundary value problem where , and our nonlinear term may be singular at .
We show that discrete exponentials form a basis of discrete holomorphic functions on a finite critical map. On a combinatorially convex set, the discrete polynomials form a basis as well.
We develop a difference equations analogue of recent results by F. Gesztesy, K. A. Makarov, and the second author relating the Evans function and Fredholm determinants of operators with semi-separable kernels.