International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 9, Pages 31256, 16 p.
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
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.