Paul W. Eloe, Youssef N. Raffoul, Christopher C. Tisdell
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.
Submitted July 21, 2005. Published October 27, 2005.
Math Subject Classifications: 34K10, 34K07.
Key Words: Delay differential equation; boundary value problem;
existence of solutions; A-solvable; 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 |
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Youssef N. Raffoul Department of Mathematics, University of Dayton Dayton, OH 45469-2316 USA e-mail: youssef.raffoul@notes.udayton.edu |
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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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