The Oscilation And Nonoscillation For Somes Kinds Of Neutral Difference Equations

The difference of the solution of the qualitative theory of differential equation is theimportant part of the theory. Now, with the modern computer of booming development,for economists, scientists, biologists and physicists, the difference equation has becomea useful and important mathematical model. As neutral difference equation and highorder difference equation are more and more extensive in real life application. Neutraldifference equation and high order difference equations are analyzed and studied withmathematics theory. Therefore, the difference of the solutions for the equations thatinvolves qualitative now most of the oscillation, asymptotic behavior, the existence of thesolutions of the theoretical study, not only has the important theory value and importantpractical value.Thesis of the second-order neutral delay difference equations, second order neutraldelay differential equations with maxima, higher-order neutral delay difference equationsand asymptotic behavior of the qualitative problem are studied. The relative topics of thispaper extend the problems studied in the literature and improved the study. Content ofeach chapter study the oscillation problems and asymptotic behavior of non oscillatorysolutions. Some results which expend and improved the conclusions in previousliteratures are obtained.Firstly, by using function of functions and absurdity, two types of second-ordernonlinear neutral delay difference equations of the problem are studied. When two typesof difference equations are studied, some sufficient conditions were given aboutequations.Secondly, for with maximum second-order difference equations, by using mainlyfunction of functions, Riccati equation, and absurdity, the oscillatory and asymptoticbehavior of solutions of with maximum second-order difference equations are studiedand several sufficient conditions are given.Finally, for the high-order nonlinear neutral delay difference equations, thedifferential inequality method and the absurdity are applied. Under the different conditions, some sufficient conditions of this equations to be oscillatory are obtained.