Integro-differential Equations with Degenerating in Banach Spaces // BSU Bulletin. Mathematics, Informatics. - 2016. №3. . - С. 3-14.

Integro-differential Equations with Degenerating in Banach Spaces

DOI: 10.18101/2304-5728-2016-3-3-14 UDK: 517.983.5, 517.968.7

In this paper integro-differential equations of the special type with Noethe- rian operator in main part in Banach spaces is investigated. All investigations conduct in space of generalized functions with value in Banach spaces and with support on positive semiaxis. In this paper instrument of fundamental op- erator-functions is application, this instrument make possible reconstruct of generalized solutions in convolution form and on this basis obtain theorem about solvability being investigated problems in set of function of finite smoothness. This method of investigations make possible automatically solve problem of agreement input data for existence of classical (smooth) solutions and also obtain formulas for representation of solutions both in spaces of dis- tributions and in spaces of functions of finite smooth. Examined in this paper integro-differential equations make possible in most general form investigated mathematical models of theory of oscillations in visco-elastic medium or of theory of electric chain.

Noetherian Operator, fundamental solution, convolution, gener- alized function.