Надіслати цю статтю Розв’язність двоточкової крайової задачі для диференціального рівняння з параметром у нелокальних умовах в уточненій соболєвській шкалі
Анотація
Досліджено нелокальну крайову задачу для диференціального рівняння з параметром. Встановлено умови розв’язності цієї задачі в просторах Хермандера, які утворюють уточнену соболєвську шкалу функцій однієї дійсної змінної. Розглядувана задача є коректною за Адамаром. Знаменники, які виникають при побудові розв’язку, не є малими і оцінюються знизу деякими додатними сталими.
Зразок для цитування: В. С. Ільків, Н. І. Страп, І. І. Волянська, “Розв’язність двоточкової крайової задачі для диференціального рівняння з параметром у нелокальних умовах в уточненій соболєвській шкалі”, Мат. методи та фіз.-мех. поля, 67, №3-4, 5-19 (2024), https://doi.org/10.15407/mmpmf2024.67.3-4.5-19
Ключові слова
Посилання
O. D. Vlasii, B. I. Ptashnyk, “Nonlocal boundary-value problem for linear partial differential equations unsolved with respect to the higher time derivative,” Ukr. Mat. Zh., 59, No. 3, 370–381 (2007) (in Ukrainian); English translation: Ukr. Math. J., 59, No. 3, 409–422 (2007), https://doi.org/10.1007/s11253-007-0026-z
V. S. Ilkiv, N. I. Strap, “Nonlocal boundary-value problem for a differential-operator equation with weak nonlinearity in the spaces of Dirichlet – Taylor series with fixed spectrum,” Mat. Met. Fiz.-Mekh. Polya, 59, No. 2, 77–85 (2016) (in Ukrainian); English translation: J. Math. Sci., 231, No. 4, 572–585 (2018), https://doi.org/10.1007/s10958-018-3835-8
V. S. Ilkiv, N. I. Strap, “Nonlocal boundary value problem for partial differential equation in a multidimensional complex domain,” Nauk. Visn. Uzhhor. Univ., Ser. Mat. Inform., 24, No. 1, 60–72 (2013) (in Ukrainian).
V. S. Ilkiv, N. I. Strap, “Solvability of a nonlocal boundary-value problem for the operator-differential equation with weak nonlinearity in a refined scale of Sobolev spaces,” Ukr. Mat. Visn., 12, No. 4, 437–456 (2015) (in Ukrainian); English translation: J. Math. Sci., 218, No. 1, 1–15 (2016), https://doi.org/10.1007/s10958-016-3006-8
V. S. Ilkiv, N. I. Strap, I. I. Volyanska, “Nonlocal boundary value problem for an equation with the differentiation operator in a refined Sobolev scale,” Mat. Met. Fiz.-Mekh. Polya, 63, No. 4, 5–16 (2020) (in Ukrainian); English translation: V. S. Ilkiv, N. I. Strap, I. I. Volyanska, “Nonlocal boundary value problem for an equation with differentiation operator in a refined Sobolev scale,” J. Math. Sci., 273, No. 6, 885–900 (2023), https://doi.org/10.1007/s10958-023-06552-5
V. S. Ilkiv, N. I. Strap, I. I. Volyanska, “Solvability conditions for the nonlocal boundary-value problem for a differential-operator equation with weak nonlinearity in the refined Sobolev scale of spaces of functions of many real variables,” Ukr. Mat. Zh., 72, No. 4, 452–466 (2020) (in Ukrainian); English translation: Ukr. Math. J., 72, No. 4, 515–535 (2020), https://doi.org/10.1007/s11253-020-01798-7
V. S. Il'kiv, N. I. Strap, I. I. Volyanska, “Conditions of solvability of the nonlocal boundary-value problem for a differential-operator equation with weak nonlinearity,” Ukr. Mat. Visn., 18, No. 1, 37–59 (2021) (in Ukrainian); English translation: J. Math. Sci., 256, No. 5, 753–769 (2021), https://doi.org/10.1007/s10958-021-05458-4
P. I. Kalenyuk, I. V. Kohut, Z. M. Nytrebych, “Problem with nonlocal two-point condition in time for a homogeneous partial differential equation of infinite order with respect to space variables,” Mat. Met. Fiz.-Mekh. Polya, 51, No. 4, 17–26 (2008) (in Ukrainian); English translation: J. Math. Sci., 167, No. 1, 1–15 (2010).
L. Yo. Kondrativ, M. M. Symotiuk, I. R. Tymkiv, “Problem with nonlocal conditions for typeless partial differential equations with constant coefficients with deviating arguments,” Prykarpat. Visn. NTSh, 1 (45), 37–44 (2018), https://pvntsh.nung.edu.ua/index.php/number/article/view/11 (in Ukrainian).
V. A. Mikhailets, A. A. Murach, “Extended Sobolev scale and elliptic operators,” Ukr. Mat. Zh., 65, No. 3, 392–404 (2013) (in Russian); English translation: Ukr. Math. J., 65, No. 3, 435–447 (2013), https://doi.org/10.1007/s11253-013-0787-5
V. Mikhailets, A. Murach, I. Chepurukhina, “Elliptic operators and boundary-value problems in spaces of generalized smoothness,” Ukr. Mat. Zh., 76, No. 9, 1331–1363 (2024), https://doi.org/10.3842/umzh.v76i9.8595 (in Ukrainian); English translation: Ukr. Math. J., 76, No. 9, 1503–1536 (2025), https://doi.org/10.1007/s11253-025-02403-5
B. Yo. Ptashnyk, V. S. Il’kiv, I. Ya. Kmit’, V. M. Polishchuk, Nonlocal Boundary-Value Problems for Partial Differential Equations [in Ukrainian], Nauk. Dumka, Kyiv (2002).
I. Ya. Savka, “Nonlocal problem with dependent coefficients in conditions for the second-order equation in time variable,” Karpat. Mat. Publ., 2, No. 2, 101–110 (2010) (in Ukrainian).
R. A. Horn, C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge (1985).
A. Anop, R. Denk, A. Murach, “Elliptic problems with rough boundary data in generalized Sobolev spaces,” Commun. Pure Appl. Anal., 20, No. 2, 697–735 (2021), https://doi.org/10.3934/cpaa.2020286
D. S. Bernstein, Matrix Mathematics: Theory, Facts, and Formulas, Princeton University Press, Princeton and Oxford (2009).
T. Goy, M. Negrych, I. Savka, “On nonlocal boundary value problem for the equation of motion of a homogeneous elastic beam with pinned-pinned ends,” Carpathian Math. Publ., 10, No. 1, 105–113 (2018), https://doi.org/10.15330/cmp.10.1.105-113
N. J. Higham, Accuracy and Stability of Numerical Algorithms, SIAM, Philadelphia (2002).
V. Los, V. Mikhailets, A. Murach, “Parabolic problems in generalized Sobolev spaces,” Commun. Pure Appl. Anal., 20, No. 10, 3605–3636 (2021), https://doi.org/10.3934/cpaa.2021123
V. A. Mikhailets, A. A. Murach, Hörmander Spaces, Interpolation, and Elliptic Problems, De Gruyter Co., Berlin–Boston (2014).
M. Modanlı, “Two numerical methods for fractional partial differential equation with nonlocal boundary value problem,” Adv. Differ. Equat., Article No. 333 (2018), https://doi.org/10.1186/s13662-018-1789-2
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