Electron. J. Diff. Eqns.,
Vol. 2005(2005), No. 121, pp. 111.
Existence, uniqueness and constructive results for
delay differential equations
Paul W. Eloe, Youssef N. Raffoul, Christopher C. Tisdell
Abstract:
Here, we investigate boundaryvalue problems (BVPs) for systems
of secondorder, ordinary, delaydifferential 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 secondorder, ordinary, delaydifferential equations
are Asolvable and may be approximated via a Galerkin method.
Finally, we provide some differential inequalities such that
solutions to our equations are unique.
Submitted July 21, 2005. Published October 27, 2005.
Math Subject Classifications: 34K10, 34K07.
Key Words: Delay differential equation; boundary value problem;
existence of solutions; Asolvable; uniqueness of solutions
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Paul W. Eloe
Department of Mathematics,
University of Dayton
Dayton, OH, USA
email: paul.eloe@notes.udayton.edu 

Youssef N. Raffoul
Department of Mathematics,
University of Dayton
Dayton, OH 454692316 USA
email: youssef.raffoul@notes.udayton.edu 

Christopher C. Tisdell
School of Mathematics
The University of New South Wales
Sydney NSW 2052, Australia
email: cct@maths.unsw.edu.au

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