A class of linear fredholm integral equations of the third kind with a degenerate kernel
The purpose of the article is to find necessary and sufficient conditions for the uniqueness and non-uniqueness, existence and non-existence of solutions of linear Fredholm integral equations of the third kind with a degenerate kernel. The author proposed a new approach for the solution of the integral equation of the third kind. The peculiarity of the problem is the fact that the integral equation of the third kind can be done for any number of singular points. On the basis of the proposed method the author has established the necessary and sufficient conditions for the existence and uniqueness of solutions of the problem. In addition we establish necessary and sufficient conditions for nonexistence and nonuniqueness of the solution of the integral equation of the third kind. Using this method, the problem is reduced to a system of linear algebraic equations. Author shows a specific example illustrating the results of this work. This example is solved on the basis of the proposed method.