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2017 | Vol. 6, iss. 4 | 306--313
Tytuł artykułu

Damped solutions of singular IVPS with Φ-Laplacian

Autorzy
Treść / Zawartość
Warianty tytułu
CS
Tlumená řešení singulární úlohy s Φ-Laplaciánem
Języki publikacji
EN
Abstrakty
EN
We study analytical properties of a singular nonlinear ordinary differential equation with a Φ-Laplacian. We investigate solutions of the initial value problem (p(t)Φ(u’(t)))’ + p(t)f(Φ(u(t))) = 0, u(0) = uₒ ϵ [Lₒ,L], u’(0) = 0 on the half-line [0,∞). Here, f is a continuous function with three zeros, function p is positive on (0,∞) and p(0) = 0. The integral ∫₀1dsds/p(s) may be divergent which yields the time singularity at t = 0. Our equation generalizes equations which appear in hydrodynamics or in the nonlinear field theory.
CS
Budeme se zabývat chováním rešení singulární obycejné diferenciální rovnice druhého rádu s Φ-Laplaciánem (p(t)Φ(u’(t)))’ + p(t)f(Φ(u(t))) = 0, u(0) = uₒ ϵ [Lₒ,L], u’(0) = 0 na poloprímce [0, ∞) za pocátecních podmínek u(0) = uₒ ϵ [Lₒ,L], u’(0) = 0 Funkce f je spojitá a má tri nulové body, funkce p je kladná na (0,1)a dále platí p(0) = 0. Integrál ∫₀1ds/p(s)) muže být divergentní, což zpusobuje singularitu v t = 0. Naše rovnice zobecnuje rovnice vyskytující se v modelech napríklad v hydrodynamice nebo v nelineární teorii pole.
Wydawca

Rocznik
Strony
306--313
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
autor
  • VŠB - Technical University of Ostrava, Department of Mathematics and Descriptive Geometry, 17. listopadu 15, 708 33, Ostrava, Czech Republic, tel.: +420 597 324 177, jakub.stryja@vsb.cz
Bibliografia
  • 1. J. Burkotová, M. Hubner, I. Rachunková, E. B. Weinmüller. “Asymptotic properties of Kneser solutions to nonlinear second order ODEs with regularly varying coefficients”, J. Appl. Math. Comp., Vol. 274, 2015, p. 65–82.
  • 2. J. Burkotová, I. Rachunková, M. Rohleder, J. Stryja. “Existence and uniqueness of damped solutions of singular IVPs with _-Laplacian”, Electron. J. Qual. Theory Differ. Equ., Vol. 2016, No. 121, 2016, p. 1–28.
  • 3. J. Burkotová, M. Rohleder, J. Stryja. “On the existence and properties of three types of solutions of singular IVPs”, Electron. J. Qual. Theory Differ. Equ. Vol. 2015, No. 29, 2015, p. 1–25.
  • 4. Z. Došlá, M. Marini, S. Matucci. “A boundary value problem on a half-line for differential equations with indefinite weight”, Commun. Appl. Anal., Vol. 15, 2011, p. 341–352.
  • 5. J. Jaroš, T. Kusano, J. V. Manojlovic. “Asymptotic analysis of positive solutions of generalized Emden-Fowler differential equations in the framework of regular variation”, Cent. Eur. J. Mathc., Vol. 11, No. 12, 2013, p. 2215–2233.
  • 6. S. Matucci, P. Rehák. “Asymptotics of decreasing solutions of coupled p-Laplacian systems in the framework of regular variation”, Ann. Mat. Pura Appl., Vol. 193, 2014, p. 837–858.
  • 7. I. Rachunková, L. Rachunek, J. Tomecek. “Existence of oscillatory solutions of singular nonlinear differential equations”, Abstr. Appl. Anal., Vol. 2011, p. 1–20.
  • 8. I. Rachunková, J. Tomecek. “Homoclinic solutions of singular nonautonomous second order differential equations”, Bound. Value Probl., Vol. 2009, p. 1–21.
  • 9. I. Rachunková, J. Tomecek. “Strictly increasing solutions of a nonlinear singular differential equation arising in hydrodynamics”, Nonlinear Anal., Vol. 72, 2010, p. 2114–2118.
  • 10. I. Rachunková, J. Tomecek, J. Stryja. “Oscillatory solutions of singular equations arising in hydrodynamics”, Adv. Difference Equ., Vol. 2010, p. 1–13.
  • 11. M. Rohleder. “On the existence of oscillatory solutions of the second order nonlinear ODE” Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. Vol. 51, No. 2, 2012, p. 107–127.
  • 12. J. Vampolová. “On existence and asymptotic properties of Kneser solutions to singular second order ODE”, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math., Vol 52, No. 1, 2013, p. 135–152.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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