ON THE NONLOCAL BOUNDARY-VALUE PROBLEM FOR ONE ORDER LOADED DIFFERENTIAL-EQUATION

This work deals with boundary value problem for the equation y'(x)+P(x)y(x) = GRAPHICS lambda(j)(x)y(x(j))+f(x), (where P(x),f(x),lambda(j)(x) are continuous functions on the interval [a, b] and n < infinity) with the boundary condition y(a) = Gy(x(0))+g, where G, g are given constants and x(0) is an element of [a, b]. In addition, if x(0) = a, then the problem is reduced to Cauchy problem for the above equation.