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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
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