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Keywords:
linear differential equations; differential polynomials; meromorphic solutions; iterated order; iterated exponent of convergence of the sequence of distinct zeros
linear differential equations; differential polynomials; meromorphic solutions; iterated order; iterated exponent of convergence of the sequence of distinct zeros
Summary:
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 $A_{1}(z)$, $A_{0}(z)$ $(\not\equiv 0)$, $F$ are meromorphic functions of finite iterated $p$-order.
References:
[1] Belaidi B.: Oscillation of fixed points of solutions of some linear differential equations. Acta. Math. Univ. Comenianae 77 (2008), 2 263--269. MR 2489196 | Zbl 1174.34528
[2] Bernal L.G.: On growth $k$-order of solutions of a complex homogeneous linear differential equations. Proc. Amer. Math. Soc. 101 (1987), 317--322. MR 0902549
[3] Cao T.B., Yi H.X.: On the complex oscillation of higher order linear differential equations with meromorphic functions. J. Syst. Sci. Complex. 20 (2007), 1 135--148. DOI 10.1007/s11424-007-9012-7 | MR 2329065
[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). MR 1792926 | Zbl 0980.30022
[5] Hayman W.K.: Meromorphic Functions. Clarendon Press, Oxford, 1964. MR 0164038 | Zbl 0667.30029
[6] Kinnunen L.: Linear differential equations with solutions of finite iterated order. Southeast Asian Bull. Math. 22 (1998), 4 385--405. MR 1811183 | Zbl 0934.34076
[7] Laine I.: Nevanlinna Theory and Complex Differential Equations. Walter de Gruyter, Berlin, New York, 1993. MR 1207139 | Zbl 0784.30002
[8] Laine I., Rieppo J.: Differential polynomials generated by linear differential equations. Complex Var. Theory Appl. 49 (2004), 12 897--911. DOI 10.1080/02781070410001701092 | MR 2101213 | Zbl 1080.34076
[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. MR 2210116 | Zbl 1094.30036
[10] Nevanlinna R.: Eindeutige Analytische Funktionen. Zweite Auflage, reprint, Die Grundlehren der mathematischen Wissenschaften, 46, Springer, Berlin-New York, 1974. MR 0344426 | Zbl 0278.30002
[11] Wang J., Yi H.X.: Fixed points and hyper order of differential polynomials generated by solutions of differential equation. Complex Var. Theory Appl. 48 (2003), 1 83--94. DOI 10.1080/0278107021000037048 | MR 1953763 | Zbl 1071.30029
[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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