On Fredholm Integral Equations of the First Kind with Nonlinear Deviation.

The problems of solvability and construction of solutions of a nonlinear Fredholm functional-integral equation of the first kind with degenerate kernel and nonlinear deviation are considered. Using the method of regularization in combination with the method of degenerate kernel, an implicit functional equation with nonlinear deviation is obtained. Since Fredholm functional-integral equation of the first kind is illposed, the boundary conditions to ensure the uniqueness of the solution is used. In order to use the method of successive approximations and prove the unique solvability, the obtained implicit functional equation is transformed to the nonlinear Volterra type functional-integral equation of the second kind. The unique solvability of the problem is proved. [ABSTRACT FROM AUTHOR]