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 ashy bines protein powder 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 deva curl arc angel 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.