Досліджено нелокальну крайову задачу для рівняння з частинними похідними з оператором узагальненого диференціювання $B=z\dfrac{\partial}{\partial z}$, який діє на функції скалярної комплексної змінної $z$. Встановлено умови розв'язності даної задачі у просторах рядів Діріхле-Тейлора, побудовано формули для розв’язку. Показано, що розглядувана задача є коректною за Адамаром. Малі знаменників, які виникають при побудові розв'язку, не є малими і оцінюються знизу деякими сталими.

[1] Goy T., Negrych M., Savka I. On nonlocal boundary value problem for the equation of motion of a
homogeneous elastic beam with pinned-pinned ends. Carpathian Mathematical Publications. 2018, 10
(1), 105-113. https://doi.org/10.15330/cmp.10.1.105-113
[2] Il'kiv, V.S., Nytrebych, Z.M., Pukach, P.Y. Nonlocal problem with moment conditions
for hyperbolic equations. Electronic J. of Differential Eq., 2017, 265, 1-9.
https://digital.library.txstate.edu/handle/10877/16066
[3] Il'kiv V.S., Strap N.I., Volyanska I.I. Conditions of solvability of the nonlocal boundary-value problem
for a differential-operator equation with weak nonlinearity. Journal of Mathematical Sciences. 2021,
256 (6), 753-769. https://doi.org/10.1007/s10958-021-05458-4
[4] Kalenyuk P.I., Baranetskij Ya.Î. Kolyasa L.I. A nonlocal problem for a differential operator of even
order with involution. Journal of Applied Analysis.2020, 26 (2), 297-307. https://doi.org/10.1515/jaa-
2020-2026
[5] Kalenyuk P.I., Kohut I.V., Nytrebych Z.M. Problem with nonlocal two-point condition in time for a
homogeneous partial differential equation of infinite order with respect to space variables Journal of
Mathematical Sciences. 2010, 167 (1), 1-15. https://doi.org/10.1007/s10958-010-9898-9
[6] Kondrativ L.Yo., Symotyuk M.M., Tymkiv I.R. Problem with nonlcal conditions for partial diffeential
equations with constant coeffcitnts with delay. Precarpathian bulletin of Shevchenko Scientific Society
Number. 2018, 1 (45), 37-44. https://pvntsh.nung.edu.ua/index.php/number/article/view/11 (in
Ukrainian)
[7] Malanchuk, O., Nytrebych, Z. Homogeneous two-point problem for PDE of the second order in
time variable and infinite order in spatial variables Open Mathematics. 2017, 15 (1), 101-110.
DOI:10.1515/math-2017-0009
[8] Ptashnyk B.I., Il'kiv V.S., Kmit' I.Ya., Polishchuk V.M. Nonlocal boundary value problems for partial
differential equations. Kyiv: Naukova dumka, 2002, 416 p. (in Ukrainian)
[9] Savka I.Ya. Nonlocal problem with dependent coeffcients in conditions for the second-order equation in
time variable Carpathian Mathematical Publications. 2010, 2 (2), 101 - 110. (in Ukrainian)
[10] Shevchuk R.V., Savka I.Y., Nytrebych Z.M. The nonlocal boundary value problem for one-dimensional
backward Kolmogorov equation and associated semigroup. Carpathian Mathematical Publications. 2019,
11 (2), 463-474. https://doi.org/10.15330/cmp.11.2.463-474
[11] Vlasii O.D., Ptashnyk B.I. Nonlocal boundary-value problem for linear partial differential equations
unsolved with respect to the higher time derivative. Ukrains'kyi Matematychnyi Zhurnal 2007, 59 (3),
370-381. http://dspace.nbuv.gov.ua/handle/123456789/164082 (in Ukrainian)
[12] Volyanska I. I., Il'kiv V. S., Symotyuk M.M. Nonlocal boundary-value problem for a second-order partial
differential equation in an unbounded strip. Ukrainian mathematical journal. 2019, 70 (10), 1585-1593.
https://doi.org/10.1007/s11253-019-01591-1