INITIAL VALUE PROBLEM FOR A NONLINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATION OF THIRD ORDER WITH A DEGENERATE KERNEL

In this paper, it is considered a third order nonlinear Fredholm integro-differential equations with initial value conditions and real parameters. A nonlinear functional-integral equations is derived. Theorem on a uniqueness and existence of the solution of the problem is proved for regular values of parameters. The method of compressing mapping in the space of continuous functions is applied. Continuous dependence on parameters of the solution of initial value problem is studied.