Boundedness And Asymptotic Behavior Of Solutions Of Several Classes Of Nonlinear Differential Equations With Delays

The integral inequality is a useful tool when we study the stability theory of differential equation , especially when we study the stability , the estimate of solution and the boundedness of differential equation . In the past few years , many scholars take on the research of this field, they have achieved many good results .In the paper , some new inequalities are established , which generalize several types of integral inequalities . Using our results and Lyapunov function , the boundedness and asymptotic behavior of some differential equations are studied .The theory of boundedness and asymptotic behavior is one of important branches of differential equations . In the field of modern applied mathematics , it has made considerable headway in recent years ,because all the structure of its emergence has deep physical background and realistic mathematical model .The thesis is divided into six sections according to contents.In chapter one , Preface .we introduce the importance of the main contents of this paper. In chapter two , we will acquired boundedness and asymptotic behavior of solutions of integro-differential equations of second order which extends the results of document [1-3 ].In chapter three , we will acquired boundedness for the solutions of second order nonhomogeneous delay differential equations which extends the results of document [8-17 ].In chapter four , Boundedness and stability of solutions for the fourth order nonlinear differential equations .In chapter five , The boundedness and asymptotic behavior of solutions of a class of integro-differential equations with deviating argument are discussed which extends the results of document [20-21 ].In chapter six , The boundedness and asymptotic behavior of solutions of higher order integro-differential equations are discussed which extends the results of document [22 ].