International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 31256, 16 pages
Some existence and uniqueness results for first-order boundary
value problems for impulsive functional differential equations
with infinite delay in Fréchet spaces
1Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga 37403, TN, USA
2Department of Mathematics, University of Sidi Bel Abbes, BP 89, Sidi Bel Abbes 2000, Algeria
Received 31 January 2006; Revised 19 May 2006; Accepted 28 May 2006
Copyright © 2006 John R. Graef and Abdelghani Ouahab. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A recent nonlinear alternative for contraction maps in
Fréchet spaces due to Frigon and Granas is used to
investigate the existence and uniqueness of solutions to
first-order boundary value problems for impulsive functional
differential equations with infinite delay. An example to
illustrate the results is included.