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Some further results on the zeros and growths of entire solutions to second order linear differential equations. (English) Zbl 0943.34076
The authors investigate the hyper-exponent of convergence of zeros and hyper-order of solutions to nonhomogeneous second-order linear differential equations. As for application they estimate the zeros, growth and fixed points of solutions to some class of differential equations.

MSC:
34M10 Oscillation, growth of solutions to ordinary differential equations in the complex domain
34M05 Entire and meromorphic solutions to ordinary differential equations in the complex domain
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[1] S. BANK AND I. LAINE, On the oscillation theory of f” + Af = 0, where A is entire, Trans. Amer. Math. Soc, 273 (1982), 351-363. · Zbl 0505.34026
[2] P. D. BARRY, On a Theorem of Besicovitch, Quart. J. Math. Oxford Ser. (2), 14 (1963), 293 302. · Zbl 0122.07602
[3] P. D. BARRY, Some theorems related to the cos /?-theorem, Proc. London Math. Soc. (3), 2 (1970), 334-360. · Zbl 0204.42302
[4] Z. X. CHEN AND C. C. YANG, On the zeros and hyper-order of meromorphic solutions of linea differential equations, Ann. Acad. Sci. Fenn. Math., 24 (1999), 215-224. · Zbl 0923.34002
[5] Z. X. CHEN AND C. C. YANG, Some oscillation theorems for linear differential equations wit meromorphic coefficients, to appear in Southeast Asian Bull. Math. · Zbl 0972.34072
[6] G. GUNDERSEN, Estimates for the logarithmic derivative of a meromorphic function, plu similar estimates, J. London Math. Soc. (2), 37 (1988), 88-104. · Zbl 0638.30030
[7] G. GUNDERSEN, Finite order solutions of second order linear differential equations, Trans Amer. Math. Soc, 305 (1988), 415-429. Zentralblatt MATH: · Zbl 0669.34010
[8] W. HAYMAN, Meromorphic Functions, Clarendon Press, Oxford, 1964 · Zbl 0115.06203
[9] W. HAYMAN, The local growth of power senes: a survey of the Wiman-Valiron method, Canad. Math. Bull., 17 (1974), 317-358 · Zbl 0314.30021
[10] Y. Z. HE AND X. Z. XIAO, Algebroid Functions and Ordinary Differential Equations, Scienc Press, 1988 (in Chinese).
[11] G. JANKAND L. VOLKMANN, Meromorphic Funktionen und Differentialgleichungen, Birkhauser, 1985
[12] K. H. KWON, On the growth of entire functions satisfying second order linear differentia equations, Bull. Korean Math. Soc, 33 (1996), 487-496. · Zbl 0863.34007
[13] L. KiNNUNEN, Linear differential equations with solutions of finite iterated order, to appear i Southeast Asian Bull. Math. · Zbl 0934.34076
[14] G. VALIRON, Lectures on the General Theory of Integral Functions, Chelsea, New York, 1949
[15] H. WITTICH, Neuere Untersuchungen Uber Eindeutige Analytische Funktionen, Spnnger, Berlin-Heidelberg-New York, 1968 · Zbl 0159.10103
[16] H. X. Yi AND C. C. YANG, The Uniqueness Theory of Meromorphic Functions, Scienc Press, Beijing, 1995 (in Chinese).
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