An ordinary integro-differential equation with a degenerate kernel and an integral condition

An ordinary integro-differential equation with a degenerate kernel and an integral condition

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We consider the questions of one value solvability of the 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 MIMULUS equation is reduced to a system of algebraic equations with complex right-hand side.After some 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 SORE THROAT SPRAY nonlinear integro-differential equations with a degenerate kernel.