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Vietnam Journal of Mathematics 35:1(2007) 43-60

 Applying Fixed Point Theory to the Initial Value Problem for the Functional Differential Equations with Finite Delay

Le Thi Phuong Ngoc

Abstract.  This paper is devoted to the study of the existence and uniqueness of strong solutions for the functional differential equations with finite delay. We also study the asymptotic stability of solutions and the existence of periodic solutions. Furthermore, under some suitable assumptions on the given functions, we prove that the solution set of the problem is nonempty, compact and connected. Our approach is based on the fixed point theory and the topological degree theory of compact vector fields.

2000 Mathematics Subject Classification: 34G20.

Keywords: The fixed point theory, the Schauder's fixed point theorem, contraction mapping.

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Published by Springer since January 2013