Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 74, pp. 1-15.

Title: Initial-value problems for first-order differential systems with
       general nonlocal conditions

Author: Octavia Nica (Babes-Bolyai Univ., Cluj, Romania)

Abstract: 
 This article concerns the existence of solutions to
 initial-value problems for nonlinear first-order differential
 systems with nonlocal conditions of functional type.
 The fixed point principles by Perov, Schauder and Leray-Schauder
 are applied to a nonlinear integral operator split into two operators,
 one  of Fredholm type and the other of Volterra type.
 The novelty in this article is combining this approach with the
 technique that uses convergent to zero matrices and vector norms.

Submitted February 17, 2012. Published May 14, 2012.
Math Subject Classifications: 34A34, 34A12, 45G10
Key Words: Nonlinear differential system;  nonlocal initial condition; 
           fixed point; vector norm; matrix convergent to zero.