On the nonlocal boundary value problem for first order loaded differential equation (Q1891436)

The paper deals with the first-order differential equation \[ y'(x)+ P(x) y(x)= \sum^n_{j= 1} \lambda_j(x) y(x_j)+ f(x),\tag{1} \] where \(P\), \(f\) and \(\lambda_j\) are continuous functions on \([a, b]\). Equation (1) was defined and studied by \textit{A. M. Nakhushev} [Differ. Uravn. 12, 103-108 (1976; Zbl 0349.45011); ibid. 19, 86-94 (1983; Zbl 0536.35080)]. The author proves the existence of a unique solution satisfying the boundary condition \(y(a)= Gy(x_0)+ g\), where \(G\), \(g\) are given constants and \(x_0\in [a, b]\).