Abstract
This paper is devoted to studying the growth problem, the zeros and fixed points distribution of the solutions of linear differential equations f″+e −z f′+Q(z)f = F(z), where Q(z) ≡ h(z)e cz and c ∊ ℝ.
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References
Gao, S. A., Chen, Z. X., Chen, T. W.: Theroy of Complex Oscillation of Linear Differential Equations, Hua Zhong (Central China) University of Science and Technology Press, 1998 (in Chinese)
Hayman, W.: Meromorphic Functions, Clarendon Press, Oxford, 1964
Hille, E.: Ordinary differential equations in the complex domain, Wiley, New York, 1976
Yi, H. X., Yang, C. C.: Uniqueness Theory of Meromorphic Functions, Pure and Applied Math. Monographs No. 32, Science Press, Beijing, 1995
Chen, Z. X., Yang, C. C.: Some further results on the zeros and the growths of entire solutions of secong order linear differential equation. Kodai Math. J., 19, 341–354 (1999)
Jank, G., Volkmann, L.: Einführung in die Theorie der ganzen und Meromorphen Funktionen mit Anwendungen auf Differentialgleichungen, Birkhäuser, Basel-Boston, 1985
Laine, I.: Nevalinna Theory and Complex Differential Equations, De Gruyter, New York, 1993
Frei, M.: Uber die subnormalen losungen der differential equation w″ + e −z w′ + (konst.)w = 0. Comment. Math. Helv., 36, 1–8 (1962)
Gundersen, G.: Finite order solutions of second order linear differential equations. Trans. Amer. Math. Soc., 305, 415–429 (1998)
Langley, J. K.: On complex oscillation and a problem of Ozawa. Kodai Math. J., 9, 430–439 (1986)
Gundersen, G.: On the question of whether f″ + e −z f′ + B(z)f = 0 can admit a solution f = 0 of finite order. Proc. R. S. E., 102A, 9–17 (1986)
Chen, Z. X.: The growth of solutions of the differential equation f″ + e −z f′ + Q(z)f = 0. (in Chinese), Science in China, Series A, 45(3), 290–300 (2002)
Gundersen, G.: Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates. J. London Math. Soc., 37(2), 88–104 (1988)
Barry, P. D.: On a theorem of Besicovitch. Quart. J. Math. Oxford Ser., 14(2), 293–302 (1963)
Besicovitch, A. S.: On integral function of order < 1. Math. Ann., 97, 677–695 (1927)
Hayman, W.: The local growth of power series: a survey of the Wiman-Valiron method. Canad. Math. Bull., 17, 317–358 (1974)
He, Y. Z., Xiao, X. Z.: Algebroid Functions and Ordinary Differential Equations, Science Press, Beijing, 1988(in Chinese)
Valiron, G.: Lectures on the General Theory of Integral Functions, Chelsea, New York, 1949
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The work is supported by Tian Yuan Fund for Mathematics (Grant No. 10426007) and also sponsored by Shanghai Postdoctoral Scientific Program.
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Li, Y.Z., Wang, J. Oscillation of solutions of linear differential equations. Acta. Math. Sin.-English Ser. 24, 167–176 (2008). https://doi.org/10.1007/s10114-007-0981-1
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DOI: https://doi.org/10.1007/s10114-007-0981-1