Abstract
We find the form of all subnormal solutions of equation (1.4). Our results generalize and improve a well-known result of Wittich about equation (1.1). Several examples are given. Higher order equations are discussed.
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S. Bank, A general theorem concerning the growth of solutions of first-order algebraic differential equations, Compositio Math. 25 (1972), 61–70.
S. Bank, Three results in the value-distribution theory of solutions of linear differential equations, Kodai Math. J. 9 (1986), 225–240.
S. Bank, On the explicit determination of certain solutions of periodic differential equations, Complex Variables (to appear).
S. Bank and I. Laine, Representations of solutions of periodic second order linear differential equations, J. Reine Angew. Math. 344 (1983), 1–21.
G. Gundersen, Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates, J. London Math. Soc. (2) 37 (1988), 88-104.
G. Gundersen, Finite order solutions of second order linear differential equations, Trans. Amer. Math. Soc. 305 (1988), 415–429.
W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964.
H. Urabe and C. C. Yang, On factorization of entire functions satisfying differential equations, Kodai Math. J. (to appear).
H. Wittich, Subnormale Lösungen der Differentialgleichung w″ +p(ez)w′ + q(ez)w = 0, Nagoya Math. J. 30 (1967), 29–37.
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Gundersen, G.G., Steinbart, E.M. Subnormal Solutions of Second Order Linear Differential Equations With Periodic Coefficients. Results. Math. 25, 270–289 (1994). https://doi.org/10.1007/BF03323411
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DOI: https://doi.org/10.1007/BF03323411