The fixed points and iterated order of some differential polynomials

Benharrat Belaidi

Commentationes Mathematicae Universitatis Carolinae (2009)

  • Volume: 50, Issue: 2, page 209-219
  • ISSN: 0010-2628

Abstract

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This paper is devoted to considering the iterated order and the fixed points of some differential polynomials generated by solutions of the differential equation f ' ' + A 1 ( z ) f ' + A 0 ( z ) f = F , where A 1 ( z ) , A 0 ( z ) ( ¬ ≡ 0 ) , F are meromorphic functions of finite iterated p -order.

How to cite

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Belaidi, Benharrat. "The fixed points and iterated order of some differential polynomials." Commentationes Mathematicae Universitatis Carolinae 50.2 (2009): 209-219. <http://eudml.org/doc/32494>.

@article{Belaidi2009,
abstract = {This paper is devoted to considering the iterated order and the fixed points of some differential polynomials generated by solutions of the differential equation \[ f^\{^\{\prime \prime \}\}+A\_\{1\}(z) f^\{^\{\prime \}\} + A\_\{0\}(z) f=F, \] where $A_\{1\}(z)$, $A_\{0\}(z)$$(\lnot \equiv 0)$, $F$ are meromorphic functions of finite iterated $p$-order.},
author = {Belaidi, Benharrat},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {linear differential equations; differential polynomials; meromorphic solutions; iterated order; iterated exponent of convergence of the sequence of distinct zeros; linear differential equation; meromorphic solution; iterated order; iterated exponent},
language = {eng},
number = {2},
pages = {209-219},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The fixed points and iterated order of some differential polynomials},
url = {http://eudml.org/doc/32494},
volume = {50},
year = {2009},
}

TY - JOUR
AU - Belaidi, Benharrat
TI - The fixed points and iterated order of some differential polynomials
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2009
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 50
IS - 2
SP - 209
EP - 219
AB - This paper is devoted to considering the iterated order and the fixed points of some differential polynomials generated by solutions of the differential equation \[ f^{^{\prime \prime }}+A_{1}(z) f^{^{\prime }} + A_{0}(z) f=F, \] where $A_{1}(z)$, $A_{0}(z)$$(\lnot \equiv 0)$, $F$ are meromorphic functions of finite iterated $p$-order.
LA - eng
KW - linear differential equations; differential polynomials; meromorphic solutions; iterated order; iterated exponent of convergence of the sequence of distinct zeros; linear differential equation; meromorphic solution; iterated order; iterated exponent
UR - http://eudml.org/doc/32494
ER -

References

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  4. Chen Z.X., The fixed points and hyper order of solutions of second order complex differential equations, Acta Math. Sci. Ser. A Chin. Ed. 20 (2000), 3 425-432 (in Chinese). (2000) Zbl0980.30022MR1792926
  5. Hayman W.K., Meromorphic Functions, Clarendon Press, Oxford, 1964. Zbl0667.30029MR0164038
  6. Kinnunen L., Linear differential equations with solutions of finite iterated order, Southeast Asian Bull. Math. 22 (1998), 4 385--405. (1998) Zbl0934.34076MR1811183
  7. Laine I., Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin, New York, 1993. Zbl0784.30002MR1207139
  8. Laine I., Rieppo J., 10.1080/02781070410001701092, Complex Var. Theory Appl. 49 (2004), 12 897--911. (2004) Zbl1080.34076MR2101213DOI10.1080/02781070410001701092
  9. 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. (2006) Zbl1094.30036MR2210116
  10. Nevanlinna R., Eindeutige Analytische Funktionen, Zweite Auflage, reprint, Die Grundlehren der mathematischen Wissenschaften, 46, Springer, Berlin-New York, 1974. Zbl0278.30002MR0344426
  11. Wang J., Yi H.X., 10.1080/0278107021000037048, Complex Var. Theory Appl. 48 (2003), 1 83--94. (2003) Zbl1071.30029MR1953763DOI10.1080/0278107021000037048
  12. Zhang Q.T., Yang C.C., The Fixed Points and Resolution Theory of Meromorphic Functions, Beijing University Press, Beijing, 1988 (in Chinese). 

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