The Qualitative Study Of Some Nonlinear Difference Equations

The objective of this thesis is to investigate the global asymptotical stability of nonlinear higher-order difference equations. By using some known results, qualitative and stability theory of nonlinear difference equations, convergence Theory and some inequality techniques; we study the existence, stability and attractivity of equilibria and the boundedness, the periodic character of all pisitive solutions of some nonlinear higher-order difference equations.First, we consider the locally asymptotically stability, the periodic character of all positive solutions and the existence, the attractiveness of the unique equilibrium of the higher order difference equationBy using limit theory and monotone theory, we obtain some sufficient conditions for the unique equilibrium has monotone solution and generalize some known results.Secondly, we investigate the boundedness, the periodicity, the global attractivity and the global asymptotical stability of the higher-order nonlinear difference equationWe show that ifα< 0, then the equilibrium (?)=α-1 is global asymptotically stable. Ifα>3, then the equilibrium (?) =α-1 is a global attractor of all pisitive solutions. Some known results are extended and improved.Finally, we deal with the global asymptotical stability, permanence, invariant interval and periodic character of the rational higher-order difference equationBy using superior and inferior limit method, convergence Theory, we give a condition under which the equilibrium is asymptotically stable. Some known general results are improved.