^{1}Gorodetskii, VV Verezhak, GP ^{1}Yuriy Fedkovych Chernivtsi National University 
Dopov. Nac. akad. nauk Ukr. 2018, 8:311 
https://doi.org/10.15407/dopovidi2018.08.003 
Section: Mathematics 
Language: Ukrainian 
Abstract: The correct solvability of a nonlocal by time multipoint problem for evolutionary equations with the Bessel operator of infinite order in generalized spaces of the type $S$ and spaces of the type $S'$ that are spaces of generalized functions of infinite order of the type of ultra distributions is proved.

Keywords: a nonlocal multipoint by time problem, Bessel operator of infinite order, generalized functions, generalized spaces of the type S 
References:
 Gel'fand, I. M. & Shylov, G. E. (1958). The spaces of basic and generalized functions. Moscow: Fizmatgiz (in Russian).
 Gorbacuk, V. I. & Gorbacuk, M. L. (1984). Boundary value problems for operator differential equations. Kiev: Naukova dumka (in Russian).
 Gorodetsky, V. V. (1998). Boundary properties in the layer of smooth solutions of equations of parabolic type. Chernivtsi: Ruta (in Ukrainian).
 Gorodetsky, V. V. (1998). The set of initial v alues of smooth solutions of differentialoperator equations of a parabolic type. Chernivtsi: Ruta (in Ukrainian).
 Gorodestky, V. V. & Martynyuk, O. V. (2013). Gel'fond–Leont'ev generalized differentiation operators in spaces of type S . Sibirsk. Mat. Zh., 54, No. 3, pp. 569584 (in Russian).
 Gurevich, B. L. (1954). Some spaces of principal and generalized functions and the Cauchy problem for finite difference schemes. Dokl. AN SSSR., 99, No. 6, pp. 893896 (in Russian).
 Gel'fand, I. M. & Shylov, G. E. (1958). Some questions in the theory of differential equations. Moscow: Fizmatizd (in Russian).
 Gotinchan, T. I. & Atamanyuk, R.M. (2001). Different forms of definitions of spaces of the type W . Nauk. visnyk Cherniv. untu: Zbirnyk nauk. prats. Vyp. 111. Matematyka (pp. 2126). Chernivtsi: Ruta (in Uk rainian).
 Gorodestky, V. V. & Martynyuk, O. V. (2013). The Cauchy problem and the twopoint problem for the evolution equations with operators of generalized differentiation. Dopov. Nac. akad. nauk Ukr., No. 3, pp. 713 (in Ukrainian).
 Horodets'kyi, V. V., Petryshyn, R. I. & Todorik o, T. S. (2015). Nonlocal problem multipoint in tim e for a class of partial differential equations of infinite order. Neliniini kolyvannia, 18, No. 3, pp. 176191 (in Ukrainian).
 Gorodetskyi, V. V. & Verezhak, G. P. (2017). Generalized of So type spaces. Bukovyn. matem. zhurn., 5, No. 12, pp. 4961 (in Ukrainian).
 Gorodetskyi, V. V. & Gotinchan, T. I. (2017). Transformation of Bessel in spaces of type So . Bukovyn. matem. zhurn., 5, No. 34, pp. 5055 (in Ukrainian).
 Levitan, B. I. (1951). Expansion in Fourier series and integrals with Bessel functions. Uspekhi Mat. Nauk., 6, Iss. 2, pp. 102143 (in Russian).