The Qualitative Study Of Several Kinds Of Higher Order Nonlinear Difference Equations

This thesis directs towards some open problems and conjectures by G.Ladas etal. We consider some properties of positive solutions of several kinds of higher order delay nonlinear difference equations, for example, boundedness and persistence, global attractivity, global asymptotic stability, permanence etc. Some known results are improved, and some conjectures by GXadas are proved partially here. We also investigate the more general situation of the open problems by G.Ladas, and push forward the study of the open problems and conjectures.The whole thesis is composed of six chapters.In the first chapter, we introduce the theoretical and practical background of problems and their researching situations. We also list some important notions and signs.In the second chapter, we consider the boundedness and persistence of a class of higher order delay nonlinear difference equation. Ultimating some known results and skills of analyzing, we obtain a sufficient condition for boundedness and persistence of its positive solutions, and improve some known results.In the third and fourth chapters, we study the attractivity of two kinds of difference equations. The sufficient conditions for attractivity are obtained by application of limit theory and monotone theory. In the application, we answer an open problem by GXadas.In the fifth chapter, we investigate a class of higher order delay nonlinear difference equation. By limit theory ,iterate theory, progression theory and some known results, we obtain some sufficient conditions for global attractivity and global asymptotic stability. We also apply our results to the rational recursive sequence, answer partially the more general situation of an open problem by G.Ladas.In the last chapter, we consider a class of discrete-time Lotka-Volterra facultative mutualism system with different delays. Some sufficient conditions for permanence and global attractivity of its positive solutions are obtained.