Existence Of Solutions For Semilinear Functional Differential Inclusions

It's an important and widely-used method that studying the existence of solutions for differential equations or inclusions by fixed points theorems. By using a fixed point theorem about condensing and multivalued maps, this paper has discussed the existence of solutions for two classes of semilinear functional differential inclusion systems with the nonlocal conditions and impulsive effects. The whole paper includes four chapters.Chapter 1 is introduction section, of which the investigation background and signification of the problem were simply introduced; Chapter 2 mainly provided the fundamental definitions, signals and basic theories about multivalued maps and integrated semigroup, which will be used in this paper. In Chapter 3, we studied the existence of solutions for a class of impulsive semi-linear neutral functional differential inclusions with the nonlocal conditions, in which the first- and second-order problems were considered respectively. And finally an example was given to show the application of the obtained theorem for the first-order problem. In Chapter 4, we discussed the existence of solutions for a class of non-densely defined neutral functional differential inclusion system with nonlocal conditions and impulsive effects. And an example was also provided at last.