one value solvability

Nonlinear the first kind Fredholm integro-differential first-order equation with degenerate kernel and nonlinear maxima

In this note, the problems of solvability and construction of solutions for a nonlinear Fredholm one-order integro-differential equation with degenerate kernel and nonlinear maxima are considered.  Using the method of degenerate kernel combined with the method of regularization, we obtain an implicit the first-order functional-differential equation  with the nonlinear maxima.  Initial boundary conditions are used to ensure the solution uniqueness.  In order to use the method of a successive approximations and prove the one value solvability, the obtained implicit functional-differential equ