Existence, uniqueness and constructive results for delay differential equations
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Date
2005-10-27
Authors
Eloe, Paul W.
Raffoul, Youssef N.
Tisdell, Christopher
Journal Title
Journal ISSN
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