Application of Nonlinear Contraction Condition for Solution of First-order Differential Systems with General Nonlocal Conditions

Abstract

This paper 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. We also give some examples in support of our results.