Initial-value problems for first-order differential systems with general nonlocal conditions. (English) Zbl 1261.34016
Summary: 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.
MSC:
34A12 | Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations |
34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
47N20 | Applications of operator theory to differential and integral equations |