Narzędzia help

Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
first previous next last
cannonical link button

http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-article-LOD6-0006-0030

Czasopismo

Journal of Applied Analysis

Tytuł artykułu

Differential polynomials generated by second order linear differential equations

Autorzy Belaidi, B.  El Farissi, A. 
Treść / Zawartość
Warianty tytułu
Języki publikacji EN
Abstrakty
EN In this paper, we study fixed points of solutions of the differential equation f" + A1 (z) f' + A0 (z) f = 0, where Aj (z) ( ≡ ≠ 0) (j = 0,1) are transcendental meromorphic functions with finite order. Instead of looking at the zeros of f (z) - z, we proceed to a slight generalization by considering zeros of g (z) -φ(z), where g is a differential polynomial in f with polynomial coefficients,φ is a small meromorphic function relative to f, while the solution f is of infinite order.
Słowa kluczowe
PL liniowe równanie rózniczkowe   meromorficzne rozwiązania   wykładnik ciągu zbieżnego okręgu zerowego  
EN linear differential equations   meromorphic solutions   hyper order   exponent of convergence of the sequence of district zeros   hyper exponent of convergence of the sequence of district zeros  
Wydawca Walter de Gruyter GmbH & Co. KG
Czasopismo Journal of Applied Analysis
Rocznik 2008
Tom Vol. 14, nr 2
Strony 259--271
Opis fizyczny Bibliogr. 17 poz.
Twórcy
autor Belaidi, B.
autor El Farissi, A.
  • Department of Mathematics Laboratory of Pure and Applied Mathematics University of Mostaganem, BELAIDI@UNIV-MOSTA.DZ
Bibliografia
[1] Chen, Z. X., Zeros of meromorphic solutions of higher order linear differential equations, Analysis (Oxford) 14 (1994), 425-438.
[2] Chen, Z. X., The fixed points and hyper order of solutions of second order complex differential equations (in Chinese), Acta Math. Sci. Ser. A Chin. Ed. 20(3) (2000), 425-432.
[3] Chen, Z. X., Shon, K. H., On the growth and fixed points of solutions of second order differential equations with meromorphic coefficients, Acta Math. Sin. (Engl. Ser.) 21(4) (2005), 753-764.
[4] Gundersen, G. G., On the. question of whether f" + e~z f` + Q (z)f = 0 can admit a solution f L 0 of finite order, Proc. Roy. Soc. Edinburg Sect. A 102 (1986), 9-17.
[5] Gundersen, G. G., Finite order solutions of second order linear differential equations. Trans. Amer. Math. Soc. 305 (1988), 415-429.
[6] Gundersen, G. G., Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates, J. London Math. Soc. (2) 37 (1988), 88-104.
[7] Hayman, W. K., Meromorphic Functions, Clarendon Press, Oxford, 1964.
[8] Hayman, W. K., The local growth of power series: a survey of the Wiman-Valiron method, Canad. Math. Bull. 17 (1974), 317-358.
[9] Kinnunen, L., Linear differential equations with solutions of finite iterated order, Southeast Asian Bull. Math. 22(4) (1998), 385-405.
[10] Laine, I., Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter. Berlin-New York, 1993.
[l1] Laine, I., Rieppo, J., Differential polynomials generated by linear differential equations, Complex Var. Theory Appl. 49(12) (2004), 897-911
[12] Liu, M. S., Zhang, X. M., Fixed points of meromorphic solutions of higher order Linear differential equations, Ann. Acad. Sci. Fenn. Math. 31 (2006), 191-211.
[13] Nevanlinna, R., Eindeutige Analytische Funktionen (in German), Zweite Auflage. Reprint. Grundlehren Math. Wiss. 46, Springer-Verlag, Berlin-New York, 1974.
[14] Valiron, G., Lectures on the General Theory of Integral Functions, Chelsea, New York, 1949.
[15] Wang, J. and Yi, H. X., Fixed points and hyper order of differential polynomials generated by solutions of differential equation, Complex Var. Theory Appl. 48(1) (2003), 83-94.
[16] Yang, C. C., Yi, H. X., Uniqueness theory of meromorphic functions, Math. Appl. 557, Kluwer Acad. Publ. Group, Dordrecht, 2003.
[17] Zhang, Q. T., Yang, C. C., The Fixed Points and Resolution Theory of Meromorphic Functions (in Chinese), Beijing Univ. Press, Beijing, 1988.
Kolekcja BazTech
Identyfikator YADDA bwmeta1.element.baztech-article-LOD6-0006-0030
Identyfikatory