Integral Inclusions In Banach Space

In this thesis , we discuss the existence of the solutions to integral inclusions in real separable Banach spaces. The main content consisted of two chapters:In the first chapter , we consider the existence of the solutions to the nonlinear integral inclusion with uncertained free termin a real separable Banach space , where F : [0,T]×X→ P_f(X) is a lower semicontin-uous multifunction with decomposable values ,f and λ are given mappings. And that we obtain one of the main results of this paper is Theorem 3.1.In the second chapter, we discuss the Filippov type existence theorem to the other nonconvex integral inclusion with uncertained free termin a real separable Banach space. Where : F : [0, T] × X → P_f(X), λ : I × C(I, X)→ X, f:I×I×X→X, V: C(I,X) → C(I,X) are given functions. We get Theorem 3.1 (one of the main results of this paper )with the contraction principle for multifunc-tions.These two results mainly extend the conclusions of reference [10] from the case with certained free term to that with uncertained free term .In this thesis, our proof is mainly based on the theories of fixed-point theorems, and multivalued analysis.