Existence of non-oscillatory solutions for a higher-order nonlinear neutral difference equation.
In this paper, we present several sufficient conditions for the existence of nonoscillatory solutions to the following third order neutral type difference equation via Banach contraction principle. Examples are provided to illustrate the main results. The results obtained in this paper extend and complement some of the existing results.
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.