Existence Of Bounded Positive Solutions For A Sixth Order Nonlinear Neutral Delay Difference Equation

This paper is devoted to the problems of the existence of uncountably many bounded positive solutions for the following sixth order nonlinear neutral delay difference equation by utilizing the Krasnoselskii's fixed point theorem and Schauder's fixed point theorem.Firstly,the importance of the study for the above sixth order nonlinear neutral delay difference equation is stated and the development of difference equation is introduced in the past few decades.Secondly,some required symbols,related definitions and important lemmas are given to prove some theorems in this paper.Thirdly,according to the different range of the real sequence {?n)n?Nn0,seven theorems are established.By means of the Krasnoselskii's fixed point theorem and Schauder's fixed point theorem,the conditions to ensure the existence of uncountably many bounded positive solutions for sixth order nonlinear neutral delay difference equation is obtained in Banach spaces.Finally,seven nontrivial examples are constructed to show the value and importance of the practical application of this article theorem.