Application of Integral Equations for the Investigation of Differential Equations

Preliminary remarks. Integral equations play an important role in the theory of ordinary and partial differential equations and boundary value problems. The reduction of boundary value problems to integral equations allows for the application of iteration and finite-difference methods of solving integral equations. These methods are, as a rule, substantially simpler than those used for solving differential equations. Moreover, many delicate proofs and qualitative results of the theory of differential equations have been obtained by the investigation of the corresponding integral equations.