Meromorphic solutions of some second order differential equations
نویسندگان
چکیده
منابع مشابه
On the Hyper-order of Solutions of Second Order Linear Differential Equations with Meromorphic Coefficients
In this paper, we investigate the growth of solutions of the linear differential equation 0 = Bf f A f , where ) (z A and 0) )( ( z B are meromorphic functions. More specifically, we estimate the lower bounded of hyperorder of solutions of the equation with respect to the conditions of ) (z A and 0) )( ( z B if solutions 0 ( f ) of the equation is of infinite order. keywords: ...
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Abstract. In this paper, we investigate the higher-order linear differential equations with meromorphic coefficients. We improve and extend a result of M.S. Liu and C.L. Yuan, by using the estimates for the logarithmic derivative of a transcendental meromorphic function due to Gundersen, and the extended Winman-Valiron theory which proved by J. Wang and H.X. Yi. In addition, we also consider th...
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i. P. Deligne, Usp. Mat. Nauk, 30, No. 5, 159-190 (1975). 2. H. Jacquet andR. P. Langlands, Automorphic Formson GL(2), Springer-Verlag (1970). 3. S. Banach,.Oeuvres, Vol. i, Warsawa (1967), pp. 318-322. 4. G. A. Margulis, Monatsh. Mmth., 9__0, No. 3, 233-235 (1980), 5. D. Sullivan, Bull. Am. Math. Soc., ~, No. i, 121-123 (1981). 6. R. A. Rank_in, Proc. Cambridge Philos. Soc., 35, 351-372 (1939)...
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where F is a polynomial in the first k+ 1 variables, whose coefficients are analytic functions of the independent variable z. If the conditions of Cauchy's theorem for the existence and uniqueness of the solution are satisfied, then (0.1) determines an analytic function in a neighbourhood of a given point z0. One of the most difficult problems in the analytic theory of differential equations is...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1993
ISSN: 0386-2194
DOI: 10.3792/pjaa.69.327