Samoilenko's method to differential algebraic systems with integral boundary conditions (Q1431917)

Consider the nonlocal boundary value problem \[ \begin{aligned} & x'=f(t,x,y),\quad y(t)=g(t,x(t),y(t)),\quad 0<t<T,\\ & A_0x(0)+\int^\zeta_0 D(s)x(s)\,ds+A_1x(T)=d,\end{aligned}\tag{*} \] where \(f\) and \(g\) are continuous, \(A_0\), \(A_1\) and \(D(s)\) are given matrices, \(d\) is a given vector, \(0<\zeta\leq T\). The author applies a method due to A. M. Samoilenko and combines it with the comparison principle to provide a constructive existence proof for (*). He generalizes his result to a system with deviating arguments.