Convergence Of Some Kinds Of Functional Differential Systems

In recent years,functional differential equations have drawn attention to many researchers.Most of the researches on functional differential equations in recent years are concentrated on the results: the existence of solutions,the existence of extremum solutions and the stability,while there are few studies on the convergence of solutions for functional differential equations.Therefore,it is of great significance to study the convergence of functional differential equations.In this paper,some kinds of functional differential equations are studied by using the comparison principle,quasilinization method and differential inequalities.The main research contents and results are as follows:In the first part,functional integral differential equations with boundary value conditions can be discussed.By defining the the coupled lower and upper solutions of nonlinear boundary value conditions and using the quasilinearization,the result of square convergence is obtained.Forthmore an example is given to illustrate the validity of the theorem.In the second part,the set-valued functional differential equation under the initial value condition can be introduced.Firstly,giving some definitions of Hukuhara derivative and partial derivatives,combining the upper and lower solutions and coupled upper and lower solutions,the comparison theorems corresponding set-valued functional differential equations are obtained.Finally we have the results of square convergence by quasilinear method.In the third part,the impulse set-valued functional integral differential equation under nonlinear boundary value condition can be investigated.Firstly,by defining several different types of coupled upper and lower solutions of the impulse set-valued functional integro-differential equation and combining monotone iteration method,some comparison theorems are given to obtain different monotone sequences.Finally we obtain the monotone sequence and have the results of uniform convergence.