Differential Equations In The Bounded Square Integrable And Lipschitz Stability

With the rapid development of science and technology, ordinary differentialequations and differential systems were studied broadly. They can be widely used inimage processing, dense analysis, molecular evolution, gene sequence and so on. Thetheory on properties of solutions of differential equations and differential systems isalready one of important aspects in applied mathematics theories. In recently yearsthe theory was paid much more attentions.In the paper, with the aid of auxiliary functions and extended Bellman-Bihariintegral inequalities, quadratic integrability and boundedness of solutions of thesecond order nonhomogeneous differential equations with delays and boundednessand Lipschitz-stability of n order nonhomogeneous differential systems with delaysare considered. The main results are generalization or improvement of the existedresults.The paper is consisted of four chapters. Chapter 1 presents the summary ofthis paper and introduces the present situation and the signiffcance of the mainproblems we have studied. Chapter 2 deals with quadratic integrability and bound-edness of solutions of a class of second order nonhomogeneous differential equationswith n-1 delays. Chapter 3 deals with quadratic integrability and boundedness ofsolutions of nth order nonlinear differential equation with delay. In last chapter weconcerned with boundedness and uniform Lipschitz-stability for solutions of a kindof n-dimensional differential systems.