Inverse Problem for a Third Order Fredholm Integro-Differential Equation with Degenerate Kernel
It is considered the questions of one value solvability of the inverse problem for a third order nonlinear partial Fredholm type integro-differential equation with degenerate kernel. The method of degenerate kernel for second kind Fredholm integral equations is modified for the case of third order partial Fredholm type integro-differential equation. The Fredholm type integro-differential equation is reduced to a system of algebraic equations. By the aid of additional condition it is obtained a second kind nonlinear Volterra type integral equation with respect to main unknown function and a first kind linear Volterra type integral equation with respect to restore function. It is used the method of compressing maps, which gave us the real method of finding the solutions - the method of successive approximations. Further is defined the restore function.