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Vietnam Journal of Mathematics 35:1(2007)
43-60
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Applying Fixed Point Theory to the Initial Value
Problem for the Functional Differential Equations with Finite Delay
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Le Thi Phuong Ngoc
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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.
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2000 Mathematics Subject Classification: 34G20.
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Keywords: The fixed point theory, the Schauder's
fixed point theorem, contraction mapping.
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Established
by Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published
by Springer since January 2013
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