Асимптотична поведінка деяких типів розв’язків диференціальних рівнянь із нелінійностями різного типу

N. P. Kolun

Анотація


Розглядається диференціальне рівняння n-го порядку, яке містить у правій частині суму доданків із правильно і швидко змінними нелінійностями, та встановлюється асимптотична поведінка деяких типів розв’язків цього рівняння.

 

Зразок для цитування: Н. П. Колун, “Асимптотична поведінка деяких типів розв’язків диференціальних рівнянь із нелінійностями різного типу,” Мат. методи та фіз.-мех. поля, 63, No. 4, 34–45 (2020), https://doi.org/10.15407/mmpmf2020.63.4.34-45

Translation: N. P. Kolun, “Asymptotic behavior of some types of solutions of differential equations with different types of nonlinearities,” J. Math. Sci., 273, No. 6, 924–938 (2023), https://doi.org/10.1007/s10958-023-06554-3


Ключові слова


нелінійності різного типу, диференціальні рівняння n-го порядку, правильно змінні нелінійності, швидко змінні нелінійності, асимптотична поведінка

Посилання


V. M. Evtukhov, Asymptotic Representation of Solutions of Nonautonomous Ordinary Differential Equations [in Russian], Doctoral Dissertation, Kiev (1998).

V. M. Evtukhov, L. A. Kirillova, “On the asymptotic behavior of solutions of nonlinear differential equations,” Differ. Uravn., 41, No. 8, 1053–1061 (2005); English translation: Differ. Equat., 41, No. 8, 1105–1114 (2005), https://doi.org/10.1007/s10625-005-0256-5

V. M. Evtukhov, A. M. Klopot, “Asymptotic representations for some classes of solutions of ordinary differential equations of order n with regularly varying nonlinearities,” Ukr. Mat. Zh., 65, No. 3, 354–380 (2013); English translation: Ukr. Math. J., 65, No. 3, 393–422 (2013), https://doi.org/10.1007/s11253-013-0785-7

V. M. Evtukhov, A. M. Klopot, “Asymptotic behavior of solutions of n th-order ordinary differential equations with regularly varying nonlinearities,” Differ. Uravn., 50, No. 5, 584–600 (2014); English translation: Differ. Equat., 50, No. 5, 581–597 (2014), https://doi.org/10.1134/S0012266114050024

V. M. Evtukhov, N. P. Kolun, “Asymptotics of the solutions of second-order differential equations with regularly and rapidly varying nonlinearities,” Nelin. Kolyv., 21, No. 3, 323–346 (2018); English translation: J. Math. Sci., 243, No. 3, 381–408 (2019), https://doi.org/10.1007/s10958-019-04546-w

V. М. Evtukhov, N. P. Kolun, “Asymptotic representations of the solutions of differential equations with regularly and rapidly varying nonlinearities,” Mat. Met. Fiz.-Mekh. Polya, 60, No. 1, 32–42 (2017); English translation: J. Math. Sci., 240, No. 1, 34–47 (2019), https://doi.org/10.1007/s10958-019-04334-6

V. M. Evtukhov, N. P. Kolun, “Rapidly varying solutions of a second order differential equation with regularly and rapidly varying nonlinearities,” Ukr. Mat. Visn., 15, No. 1, 18–42 (2018); English translation: J. Math. Sci., 235, No. 1, 15–34 (2018), https://doi.org/10.1007/s10958-018-4055-y

V. M. Evtukhov, A. M. Samoilenko, “Asymptotic representations of solutions of nonautonomous ordinary differential equations with regularly varying nonlinearities,” Differ. Uravn., 47, No. 5, 628–650 (2011); English translation: Differ. Equat., 47, No. 5, 627–649 (2011), https://doi.org/10.1134/S001226611105003X

V. M. Evtukhov, A. M. Samoilenko, “Conditions for the existence of solutions of real nonautonomous systems of quasilinear differential equations vanishing at a singular point,” Ukr. Mat. Zh., 62, No. 1, 52–80 (2010); English translation: Ukr. Math. J., 62, No. 1, 56–86 (2010), https://doi.org/10.1007/s11253-010-0333-7

A. M. Klopot, “Asymptotic behavior of solutions of n-th order nonautonomous ordinary differential equations with regularly varying nonlinearities,” Visn. Odes’k. Nats. Univ., Ser. Matem. Mekh., 18, No. 3(19), 16–34 (2013) (in Russian).

A. M. Klopot, “On the asymptotics of solutions of nonautonomous differential equations of order n,” Nelin. Kolyv., 15, No. 4, 447–465 (2012); English translation: J. Math. Sci., 194, No. 4, 354–373 (2013), https://doi.org/10.1007/s10958-013-1534-z

N. P. Kolun, “Asymptotics of slowly varying solutions of second-order differential equations with regularly and rapidly varying nonlinearities,” Doslidzhennia v matematytsi i mekhanitsi, 23, No. 2(32), 54–67 (2018) (in Ukrainian), https://doi.org/10.18524/2519-206x.2018.2(32).149704

N. P. Kolun, “Asymptotic behavior of solutions of second-order differential equations with nonlinearities of different types,” Nauk. Visn. Uzhhorod. Nats. Univ., Ser. Matem. Inform., No. 1(34), 26–41 (2019) (in Ukrainian).

N. P. Kolun, “Asymptotic representation of slowly varying solutions of second-order differential equations with nonlinearities of different types in the right-hand side,” Bukov. Mat. Zh., 6, No. 3-4, 89–102 (2018) (in Ukrainian), https://doi.org/10.31861/bmj2018.03.089

E. Seneta, Regularly Varying Functions, Lect. Notes Math., Vol. 508, 1976.

S. Cano-Casanova, “Decay rate at infinity of the positive solutions of a generalized class of Thomas – Fermi equations,” in: Proc. 8th AIMS Conf. Discrete Cont. Dynam. Systems Differ. Equat. Suppl. 2011, Vol. 1, 240–249 (2011), https://doi.org/10.3934/proc.2011.2011.240

V. M. Evtukhov, A. M. Klopot, “Asymptotic behavior of solutions of ordinary differential equations of n-th order with regularly varying nonlinearities,” Mem. Differ. Equat. Math. Phys., 61, 37–61 (2014).

V. M. Evtukhov, N. P. Kolun, “Asymptotic behaviour of solutions of second-order nonlinear differential equations,” Mem. Differ. Equat. Math. Phys., 75, 105–114 (2018).

T. Kusano, J. V. Manojlović, V. Marić, “Increasing solutions of Thomas–Fermi type differential equations – The sublinear case,” Bull. de l’Acad. Serbe des Sci. et des Arts. – Classe des Sciences Mathematiques et Naturelles. Sciences mathematiques, CXLIII, No. 36, 21–36 (2011).

J. V. Manojlović, V. Marić, “An asymptotic analysis of positive solutions of Thomas–Fermi type sublinear differential equations,” Mem. Differ. Equat. Math. Phys., 57, 75–94 (2012).

V. Marić, Regular Variation and Differential Equations, Lect. Notes Math., Vol. 1726, Springer–Verlag, Berlin–Heidelberg (2000).

V. Marić, Z. Radašin, “Asymptotic behavior of solutions of the equation y′′=f(t)φ(ψ(y)),” Glasnik matematički, 23 (43), No. 1, 27–34 (1988).

V. Marić, M. Tomić, “Asymptotics of solutions of a generalized Thomas – Fermi equations,” J. Differ. Equat., 35, No. 1, 36–44 (1980), https://doi.org/10.1016/0022-0396(80)90047-9

S. D. Taliaferro, “Asymptotic behavior of positive decreasing solutions of y′′=F(t,y,y′),” in: Geometric analysis and nonlinear PDE: Lect. Notes in Pure and Appl. Math., Vol. 144, Ed. I. J. Bakelman, M. Dekker, New York (1993), pp. 105–127.

S. D. Taliaferro, “Asymptotic behavior of solutions of y′′=φ(t)f(y),” SIAM J. Math. Anal., 12, No. 6, 853–865 (1981), https://doi.org/10.1137/0512071


Повний текст: PDF

Посилання

  • Поки немає зовнішніх посилань.


Creative Commons License
Ця робота ліцензована Creative Commons Attribution 3.0 License.