A nonlocal problem multipoint by time for one class of evolutionary singular equations

1Gorodetskii, VV, 1Martynyuk, OV
1Yuriy Fedkovych Chernivtsi National University
Dopov. Nac. akad. nauk Ukr. 2018, 5:8-15
Section: Mathematics
Language: Ukrainian

The solvability of a nonlocal problem multipoint by time for evolutionary equations with pseudo-Bessel infinite-order operators with an initial condition that is an element of the space of generalized functions of the dis tribution type is established in the case where the nonlocal multipoint condition contains pseudo-Bessel ope rators.

Keywords: countably normed space, evolutionary equations, nonlocal problem multipoint by time, pseudodifferential operator
  1. Nahushev, A. M. (1995). The equations of mathematical biology. Moscow: Vysshaya shkola (in Russian).
  2. Belavin, I. A., Kapitsa, S. P. & Kurdyumov, S. P. (1998). The mathematical model of global demographic proccesses with considering of space distribution. Zhurn. vychisl. matem. mat. fiz., 38, No. 6, pp. 885-902 (in Russian).
  3. Dezin, A. A. (1980). General questions of the theory of boundary-value problems. Moscow: Nauka (in Russian).
  4. Romanko, V. K. (1974). Boundary-value problems for one class of differential operators. Differents. uravneniya, 10, No. 11, pp. 117-131 (in Russian).
  5. Romanko, V. K. (1985). Nonlocal boundary value problems for certain systems of equations. Matem. zametki, 37, No. 7, pp. 727-733 (in Russian).
  6. Makarov, A. A. (1994). The existence of a correct two-point boundary-value problem in a layer for systems of pseudodifferential equations. Differents. uravneniya, 30, No. 1, pp. 144-150 (in Russian).
  7. Chesalin, V. I. (1979). The problem with nonlocal boundary conditions for some abstract hyperbolic equations. Differents. uravneniya, 15, No. 11, pp. 2104-2106 (in Russian).
  8. Il'kiv, V. S. & Ptashnyk, B. I. (2005). A nonlocal two-point problem for systems of partial differential equations. Sibir. mat. zhurn., 46, No. 11, pp. 119-129 (in Russian).
  9. Chabrouski, J. (1984). On the non-local problems with a functional for parabolic equation. Funckcialaj Ekvacioj, 27, pp. 101-123.
  10. Gorodetskii, V. V. & Todoriko, T. S. (2011). Investigation of the properties of solutions of a nonlocal multipoint for a time problem for a class of singular evolutionary equations. Scientific Herald of Yuriy Fedkovych Chernivtsi National University, Ser. Math., 1, No. 4, pp. 29-35 (in Ukrainian).
  11. Kulyk, T.S. & Myronyk, V.I. (2011). Multipoint problem for a class of evolutionary pseudodifferential equations of a parabolic type. Scientific Herald of Yuriy Fedkovych Chernivtsi National University, Ser. Math. 1, No. 3, pp. 49-57 (in Ukrainian).
  12. Gorodetskii, V.V. & Lenyuk, O.M. (2007). Fourier-Bessel transform for one class of infinitely differential functions. Boundary problems for differential equations: Collection of sciences. Chernivtsi: Prut. Iss. 15, pp. 51-66 (in Ukrainian).
  13. Zhytomyrskiy, Ya.I. (1955). The Cauchy problem for systems of linear partial differential equations with a differential Bessel operator. Matem. sb., 36, No. 2, pp. 299-310 (in Russian).
  14. Lenyuk, O.M. (2007). Bessel transformation of a class of generalized functions of distribution type. Scientific Herald of Yuriy Fedkovych Chernivtsi National University, Ser. Math., Iss. 336-337, pp. 95-102 (in Ukrainian).
  15. Gorodetskii, V.V. & Myronyk, V.I. (2010). A two-point problem for a class of evolutionary equations. I. Differents. uravneniya, 46, No. 3, pp. 349-363 (in Russian).