Надіслати цю статтю Асимптотические представления решений дифференциальных уравнений с правильно и быстро меняющимися нелинейностями
Анотація
Устанавливаются асимптотические свойства некоторых типов решений дифференциальных уравнений второго порядка, которые содержат в правой части сумму слагаемых с правильно и быстро меняющимися нелинейностями.
Евтухов В. М., Колун Н. П. Асимптотические представления решений дифференциальных уравнений с правильно и быстро меняющимися нелинейностями // Мат. методи та фіз.-мех. поля. – 2017. – 60, № 1. – С. 32–42.
Translation: Evtukhov V. М., Kolun N. P. Asymptotic representations of the solutions of differential equations with regularly and rapidly varying nonlinearities // J. Math. Sci. – 2019. – 240, No. 1. – P. 34–47. – https://doi.org/10.1007/s10958-019-04334-6
Ключові слова
Посилання
Evtukhov V.M. Asimptoticheskie predstavleniya resheniy neavtonomnyih obyiknovennyih differentsialnyih uravneniy. Diss….d. fiz.-mat. nauk. Kiev, 1998. – 295 s.
Evtukhov V.M., Vladova E.S. Asimptoticheskie predstavleniya resheniy suschestvenno nelineynyih tsiklicheskih sistem obyiknovennyih differentsialnyih uravneniy // Differents. uravneniya. – 2012. – 48, № 5. – S. 622–639.
To zhe: Evtukhov V.M., Vladova E.S. Asymptotic representations of solutions of essentially nonlinear cyclic systems of ordinary differential equations // Differential Equations – 2012. – 48, No. 5.– P. 630–646.
Evtukhov V.M., Kirillova M.A. Ob asimptotike resheniy nelineynyih differentsialnyih uravneniy vtorogo poryadka // Differents. uravneniya – 2005. – 41, № 8. – S. 1053–1061.
To zhe: Evtukhov V.M., Kirillova L.A. On the asymptotics of solutions of nonlinear second-order differential equations // Differential Equations – 2005. – 41, No. 8.– P. 1105–1114.
Evtukhov V.M., Klopot A.M. Asimptoticheskoe povedenie resheniy obyiknovennyih differentsialnyih uravneniy n-togo poryadka s pravilno menyayuschimisya nelineynostyami // Differents. uravneniya – 2014. – 50, №5. – S. 584–600.
To zhe: Evtukhov V.M., Klopot A.M. Asymptotic behavior of solutions of nth-order ordinary differential equations with regularly varying nonlinearities // Differential Equations – 2014. – 50, No. 5.– P. 581–597.
Evtukhov V.M., Samoylenko A.M. Asimptoticheskie predstavleniya resheniy neavtonomnyih obyiknovennyih diferentsialnyih uravneniy s pravilno menyayuschimisya nelineynostyami // Differents. uravneniya. – 2011. – 47, № 5. – S. 628–650.
Evtukhov V.M., Samoylenko A.M. Usloviya suschestvovaniya ischezayuschih v osoboy tochke resheniy u veschestvennyih neavtonomnyih sistem kvazilineynyih differentsialnyih uravneniy // Ukr. mat. zhurn. – 2010. – 62, № 1. – S. 52–80.
To zhe: Evtukhov V.M., Samoilenko A.M. Conditions for the existence of solutions of real nonautonomous systems of quasilinear differential equations vanishing at a singular point // Ukr. Math. J. – 2010. – 62, No. 1. – P. 56–86.
Evtukhov V.M., Harkov V.M. Asimptoticheskie predstavleniya resheniy suschestvenno nelineynyih differentsialnyih uravneniy vtorogo poryadka // Differents. uravneniya – 2007. – 43, № 9. – S. 1311–1323.
To zhe: Evtukhov V.M., Kharkov V.M. Asymptotic representations of solutions of essentially nonlinear second-order differential equations // Differential Equations – 2007. – 43, No. 10.– P. 1340–1352.
Kasyanova V.A. Asimptoticheskie predstavleniya resheniy neavtonomnyih obyiknovennyih differentsialnyih uravneniy vtorogo poryadka s nelineynostyami, asimptoticheski blizkimi k stepennyim. Diss….kand. fiz.-mat. nauk. Odessa, 2009. – 154 s.
Chernikova A.G. Asimptotika byistro izmenyayuschihsya resheniy differentsialnyih uravneniy vtorogo poryadka s byistro menyayuscheysya nelineynostyu // VIsnik Od. nats. un-tu. Mat. I meh. – 2015. – 20, №2. – S. 52–68.
Seneta E. Pravilno menyayuschiesya funktsii. – M.: Nauka, 1985. – 144 s.
Cano-Casanova S. Decay rate at infinity of the positive solutions of a generalised class of Thomas-Fermi equations // 8th AIMS Conference, Discrete Contin. Dyn. Syst. Syppl. – 2011. – 1, P. 240–249.
Kusano T., Manojlović J., Marić V. Increasing solutions of Thomas-Fermi type differential equations – the sublinear case // Bull. T. de Acad. Serbe Sci. Arts, Classe Sci. Mat. Nat., Sci. Math. – 2011. – CXLIII, No. 36. – P. 21–36.
Manojlović J., Marić V. An asymptotic analysis of positive solutions of Thomas-Fermi type sublinear differential equations // Mem. Differential Equations Math. Phys. – 2012. – 57, P. 75–94.
Marić V. Regular Variation and Differential Equations. Lecture Notes in Mathematics 1726. Springer-Verlag, Berlin Heidelberg. – 2000. – 128 p.
Marić V., Radaŝin Asymptotic behavior of solutions of the equation y"=f(t)Φ(Ψ(y)) // Glasnik matematički – 1988. – 23 (43), P. 27–34.
Marić V., Tomić M. Asymptotics of solutions of a generalised Thomas-Fermi equations // Differential Equations – 1980. – 35, No. 1.– P. 36–44.
Řehák P., Matucci S. Extremal solutions to a system of n nonlinear differential equations and regularly varying functions // Math. Nachr. – 2015. – 288, No. 11-12.– P. 1413–1430.
Taliaferro S.D. Asymptotic behavior of solutions of y"=φ(t)f(y). // SIAM J. Math. Anal. – 1981. – 12, No. 6.– P. 853–865.
Taliaferro S.D. Asymptotic behavior of positive decreasing solutions of y"=F(y,yˊ,y") // Geometric analysis and nonlinear PDE. Lecture notes in pure and appl. math. M.Dekker New York. – 1993. – P. 105 – 127.
Посилання
- Поки немає зовнішніх посилань.
Ця робота ліцензована Creative Commons Attribution 3.0 License.