Existence, uniqueness and constructive results for delay differential equations

Date

2005-10-27

Authors

Eloe, Paul W.
Raffoul, Youssef N.
Tisdell, Christopher

Journal Title

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Volume Title

Publisher

Texas State University-San Marcos, Department of Mathematics

Abstract

Here, we investigate boundary-value problems (BVPs) for systems of second-order, ordinary, delay-differential equations. We introduce some differential inequalities such that all solutions (and their derivatives) to a certain family of BVPs satisfy some a priori bounds. The results are then applied, in conjunction with topological arguments, to prove the existence of solutions. We then apply earlier abstract theory of Petryshyn to formulate some constructive results under which solutions to BVPs for systems of second-order, ordinary, delay-differential equations are A-solvable and may be approximated via a Galerkin method. Finally, we provide some differential inequalities such that solutions to our equations are unique.

Description

Keywords

Delay differential equations, Boundary value problems, Existence of solutions, A-solvable, Uniqueness of solutions

Citation

Eloe, P. W., Raffoul, Y. N., & Tisdell, C. C. (2005). Existence, uniqueness and constructive results for delay differential equations. <i>Electronic Journal of Differential Equations, 2005</i>(121), pp. 1-11.

Rights

Attribution 4.0 International

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