Oscillation Of Several Kinds Of Neutral Difference Equations With Delay

Differential equations are powerful tool which is used to describe the variation of natural phenomenon. We usually regard corresponding difference equation as the discrete form of differential equations, but it also has its own particularity. As the development of computer science and technology, in many disciplines, such as control engineering, medicine, modern physics, biomathematics, the neutral difference equations are frequently proposed. The oscillation of difference equations is an important content in qualitative theory of difference equations, so the research about the oscillation of neutral difference equations is not only the needs of the development of the mathematical theory itself, but also the need of the practical application. This paper separately discusses the oscillation of all solutions of a neutral delay difference equation with constant coefficient, with variable coefficient, and with positive and negative coefficients. This paper is divided into the following sections:The first chapter introduces the research background and basic definitions of the several kinds of neutral delay difference equations, and the main research content in this paper.The second chapter discusses the first-order functional differential equation with constant coefficient such that and obtain a sufficient condition for the oscillation of all solutions for this equation.Through discussing the neutral delay difference equation such thatSome necessary and sufficient conditions for the oscillation of all solutions for this equation can be obtained, and some conclusions are extended.The third chapter discusses the oscillation of a second order non-linear neutral delay difference equations with variable coefficients such that and obtained some new theorems to judge oscillation of all solutions for this equation.The fourth chapter discusses a neutral delay difference equation with positive and negative coefficients such thatSome sufficient conditions can be obtained to judge oscillation of all solutions for this equation.