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2013 | 11 | 12 | 2215-2233
Tytuł artykułu

Asymptotic analysis of positive solutions of generalized Emden-Fowler differential equations in the framework of regular variation

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Języki publikacji
EN
Abstrakty
EN
Positive solutions of the nonlinear second-order differential equation $(p(t)|x'|^{\alpha - 1} x')' + q(t)|x|^{\beta - 1} x = 0,\alpha > \beta > 0,$ are studied under the assumption that p, q are generalized regularly varying functions. An application of the theory of regular variation gives the possibility of obtaining necessary and sufficient conditions for existence of three possible types of intermediate solutions, together with the precise information about asymptotic behavior at infinity of all solutions belonging to each type of solution classes.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
12
Strony
2215-2233
Opis fizyczny
Daty
wydano
2013-12-01
online
2013-10-08
Twórcy
Bibliografia
  • [1] Bingham N.H., Goldie C.M., Teugels J.L., Regular Variation, Encyclopedia Math. Appl., 27, Cambridge University Press, Cambridge, 1987 http://dx.doi.org/10.1017/CBO9780511721434
  • [2] Elbert Á., Kusano T., Oscillation and nonoscillation theorems for a class of second order quasilinear differential equations, Acta Math. Hungar., 1990, 56(3–4), 325–336 http://dx.doi.org/10.1007/BF01903849
  • [3] Haupt O., Differential- und Integralrechnung, Walter de Gruyter, Berlin, 1938
  • [4] Howard H.C., Maric V., Regularity and nonoscillation of solutions of second order linear differential equations, Bull. Cl. Sci. Math. Nat. Sci. Math., 1997, 22, 85–98
  • [5] Jaroš J., Kusano T., Self-adjoint differential equations and generalized Karamata functions, Bull. Cl. Sci. Math. Nat. Sci. Math., 2004, 29, 25–60
  • [6] Jaroš J., Kusano T., Tanigawa T., Nonoscillatory half-linear differential equations and generalized Karamata functions, Nonlinear Anal., 2006, 64(4), 762–787 http://dx.doi.org/10.1016/j.na.2005.05.045
  • [7] Kamo K., Usami H., Asymptotic forms of weakly increasing positive solutions for quasilinear ordinary differential equations, Electron. J. Differential Equations, 2007, #126
  • [8] Kusano T., Manojlovic J., Asymptotic behavior of positive solutions of sublinear differential equations of Emden-Fowler type, Comput. Math. Appl., 2011, 62(2), 551–565 http://dx.doi.org/10.1016/j.camwa.2011.05.019
  • [9] Kusano T., Manojlovic J.V., Maric V., Increasing solutions of Thomas-Fermi type differential equations - the sublinear case, Bull. Cl. Sci. Math. Nat. Sci. Math., 2011, 36, 21–36
  • [10] Kusano T., Maric V., Tanigawa T., An asymptotic analysis of positive solutions of generalized Thomas-Fermi differential equations - the sub-half-linear case, Nonlinear Anal., 2012, 75(4), 2474–2485 http://dx.doi.org/10.1016/j.na.2011.10.039
  • [11] Kusano T., Ogata A., Usami H., Oscillation theory for a class of second order quasilinear ordinary differential equations with application to partial differential equations, Japan. J. Math., 1993, 19(1), 131–147
  • [12] Manojlovic J., Maric V., An asymptotic analysis of positive solutions of Thomas-Fermi type sublinear differential equations, Mem. Differential Equations Math. Phys., 2012, 57, 75–94
  • [13] Maric V., Regular Variation and Differential Equations, Lecture Notes in Math., 1726, Springer, Berlin, 2000 http://dx.doi.org/10.1007/BFb0103952
  • [14] Maric V., Tomic M., A classification of solutions of second order linear differential equations by means of regularly varying functions, Publ. Inst. Math. (Beograd), 1990, 48(62), 199–207
  • [15] Naito M., On the asymptotic behavior of nonoscillatory solutions of second order quasilinear ordinary differential equations, J. Math. Anal. Appl., 2011, 381(1), 315–327 http://dx.doi.org/10.1016/j.jmaa.2011.04.006
  • [16] Seneta E., Regularly Varying Functions, Lecture Notes in Math., 508, Springer, Berlin-New York, 1976 http://dx.doi.org/10.1007/BFb0079658
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0306-9
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