International Journal of Mathematics and Mathematical Sciences 
Volume 2006 (2006), Article ID 31256, 16 pages
doi:10.1155/IJMMS/2006/31256

Some existence and uniqueness results for first-order boundary value problems for impulsive functional differential equations with infinite delay in Fréchet spaces

John R. Graef1 and Abdelghani Ouahab2

 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

Abstract

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.