|1Gorodetskii, VV, Verezhak, GP |
1Yuriy Fedkovych Chernivtsi National University
|Dopov. Nac. akad. nauk Ukr. 2018, 8:3-11|
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|
- 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 differential-operator 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. 569-584 (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. 893-896 (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. un-tu: Zbirnyk nauk. prats. Vyp. 111. Matematyka (pp. 21-26). Chernivtsi: Ruta (in Uk- rainian).
- Gorodestky, V. V. & Martynyuk, O. V. (2013). The Cauchy problem and the two-point problem for the evolution equations with operators of generalized differentiation. Dopov. Nac. akad. nauk Ukr., No. 3, pp. 7-13 (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. 176-191 (in Ukrainian).
- Gorodetskyi, V. V. & Verezhak, G. P. (2017). Generalized of So type spaces. Bukovyn. matem. zhurn., 5, No. 1-2, pp. 49-61 (in Ukrainian).
- Gorodetskyi, V. V. & Gotinchan, T. I. (2017). Transformation of Bessel in spaces of type So . Bukovyn. matem. zhurn., 5, No. 3-4, pp. 50-55 (in Ukrainian).
- Levitan, B. I. (1951). Expansion in Fourier series and integrals with Bessel functions. Uspekhi Mat. Nauk., 6, Iss. 2, pp. 102-143 (in Russian).