NONLINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATION WITH DEGENERATE KERNEL AND NONLINEAR MAXIMA - Yuldashev, Tursun; Holmanova, Klara (Журнал математики и информатики, 2021)
The initial value problem of solvability and construction of solutions of a nonlinear Fredholm integro-differential equation of first order with degenerate kernel and nonlinear maxima are considered. Using the method of degenerate kernel in combination it with the method of regularization, we obtain an implicit functional-differential equation of first order with nonlinear maxima. We use initial boundary conditions to ensure the uniqueness of the solution. In order to use the method of a successive approximations and prove the one value solvability, we transform the obtained implicit functional-differential equation to the nonlinear Volterra type integro-differential equation with nonlinear maxima. The one value solvability of the problem is proved.