Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 121, pp. 1-11.

Title: Existence, uniqueness and constructive results for
       delay differential equations
       
Authors: Paul W. Eloe (Univ. of Dayton, Dayton, OH, USA)
         Youssef N. Raffoul (Univ. of Dayton, Dayton, OH, USA)
	 Christopher C. Tisdell (Univ. New South Wales, Sydney, Australia)

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