Singular integral equation equivalent in the space of smooth functions to an ordinary differential equation, method of successive approximations for the construction of its smooth solutions and its nonsmooth solutions

• Date: 2019
• Main Authors: Samoilenko, A. M., Самойленко, А. М.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2019
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1456
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We propose a singular integral equation whose definition is extended to a singular point by additional conditions. In the space of smooth functions, this equation becomes equivalent, by the indicated extended definition, to an ordinary differential equation, whereas in the space of piecewise discont...