We consider the questions of one value solvability of the here nonlocal boundary value problem for a nonlinear ordinary integro-differential equation with a degenerate kernel and a reflective argument.The method of the degenerate kernel is developed for the case of considering ordinary integro-differential equation of the first order.After denoting the integro-differential equation is reduced to a system of algebraic equations with complex right-hand side.After some gotrax handlebar transformation we obtaine the nonlinear functional-integral equation, which one valued solvability is proved by the method of successive approximations combined with the method of compressing mapping.
This paper advances the theory of nonlinear integro-differential equations with a degenerate kernel.