Existence results for systems with nonlinear coupled nonlocal initial conditions

Abstract

The purpose of the present work is to study the existence of solutions to initial value problems for nonlinear first order differential systems with nonlinear nonlocal boundary conditions of functional type. The existence results are established by means of the Perov, Schauder and Leray-Schauder fixed point principles combined with a technique based on vector-valued metrics and convergent to zero matrices.