Qualitative Research And Applications Of Some Classes Of Impulsive Functional Differential Equations

This thesis mainly studies the practical stability of impulsive functional differential equations with finite or infinite delays,the boundedness and the periodicty for impulsive functional differential equations with applications to impulsive delayed neural networks,and the existence of solutions for impulsive boundary value problems.It is consisted of four chapters.As the introductions,in Chapter 1,the background and history of practical stability and periodicty for impulsive functional differential equations and impulsive boundary value problems are briefly addressed,and the main work of this paper are given.Chapter 2 mainly considers the practical stability of impulsive functional differential equations with finite or infinite delays,by using Lyapunov like functions with Razumikhin techniques or Lyapunov like functionals and impulsive integral inequalities,some criteria on practical stability are established,and some examples are given to illustrate our results,our results are new.In Chapter 3,we focuses on the boundedness and the periodicity for impulsive functional differential equations with finite or infinite delays.By using component Lyapunov functions or Lyapunov functionals with impulsive integral inequalities and Hale-Yoshizawa type criteria,some sufficient conditions for boundedness and existence of periodic solutions are given.As applications of our results,in section 3.3,we investigate the existence of periodic solutions and golbal exponential stability of some classes of impulsive cellular neural networks with time delays.In Chapter 4,firstly,by using Krasnoselskill's fixed point theory,we discuss periodic boundary value problems for a class of first-order singular impulsive functional differential equations which admites that function f(t,μ) may be sinluar atμ=0,some sufficient conditons for existence of positive solutions are obtained. Secondly,in section 4.2,we focuses on the existence of extreme soltions of nonlinear three-point boundary value problems for a class of impulsive functional diffeential equations,By using an impulsive differential inequality,we obtain two new comparsion results,and using the method of upper and lower solutions coupled with monotone iterative technique,we obtain the existence of extremal solution about nonlinear three-point boundary value problems.Finally,in setion 4.3,we deal with the existence of extreme solutions of integral boundary value problems for a class of first order impulsive integro-differential equations of mixed type.some interesting results are obtained.