Converse Lyapunov Theorems And Massera’s Theorems For Measure Functional Differential Equations With Infinite Delay

In this dissertation,we mainly study the regular stability and periodic solutions of measure functional differential equations with infinite delay.Firstly,by using the equivalence relation between measure functional differential equations with infinite delay and generalized ordinary differential equations under some certain conditions,combining with Lyapunov functional,the converse Lyapunov theorems of regular stability for measure functional differential equations with infinite delay are established.Furthermore,the existence of bounded solutions for measure functional differential equations with infinite delay means the existence of periodic solutions for measure functional differential equations with infinite delay is discussed,the Massera theorems of measure functional differential equations with infinite delay are established.