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Chung-Chun Yang 《Annali di Matematica Pura ed Applicata》1971,91(1):41-52
Summary In this paper we investigate the rate of growth of meromorphic functions f which are solutions of certain algebraic differential
equation whose coefficients a(z) are arbitrary meromorphic functions. By method based on Nevanlinna's theory of meromorphic
functions, it has been shown that if the zeros and poles of f satisfy the condition N(r, f′/f)=S(r, f′/f) then the ratio T(r,
f′/f)/(T(r, a(z)), as r → ∞ outside a set of r values of finite measure, is bounded for at least one of the coefficients a(z).
The content of an invited address delivered by the author on March 27, 1971 to the 683th meeting of the American Mathematical
Society of the University of Illinois at Chicago Circle, Chicago, Illinois, U.S.A.
Entrato in Redazione il 16 novembre 1970. 相似文献
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Gary G. Gundersen 《Results in Mathematics》1989,16(1-2):54-76
We use the spread relation to prove estimates that contain the Nevanlinna deficiencies of values of meromorphic solutions of certain differential equations of the form (1.1) below. We construct examples which show that all of our estimates are sharp, and in most of these constructions we use functions which are extremal for the spread relation. Several other examples are also given to illustrate our results. 相似文献
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In this paper, the growth of the meromorphic solutions of the equation
where L, M, N are birational functions, is studied. We prove that if L(z, f) satisfies a quite general condition, then f
must be of finite order. Furthermore, if (L(z, f)≡0, and M(z, f), N(z, f) are polynomials in f, then the order of any entire
solution of the equation is a positive integral multiple of 1/2.
Entrata in Redazione il 15 marzo 1999.
The research was partially supported by a UGC grant of Hong Kong (Project No: HKUST 712/96p). 相似文献
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On meromorphic solutions of first-order differential equations 总被引:1,自引:0,他引:1
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高凌云 《数学物理学报(B辑英文版)》2011,31(2):541-548
Using the Nevanlinna theory of the value distribution of meromorphic functions and theory of differential algebra, we investigate the problem of the forms of meromorphic solutions of some specific systems of generalized higher order algebraic differential equations with exponential coefficients and obtain some results. 相似文献
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Yuichi Sakai 《The Ramanujan Journal》2010,22(3):261-272
Kaneko and Koike gave the “extremal” quasimodular forms of depth 1 for PSL2(ℤ) and modular differential equations they satisfy. In this paper, we study modular solutions of their modular differential
equations. 相似文献
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The main purpose of this article is to study the existence theories of global meromorphic solutions for some second-order linear differential equations with meromorphic coefficients, which perfect the solution theory of such equations. 相似文献
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LIYEZHOU CHENZONGXUAN 《高校应用数学学报(英文版)》1998,13(4):403-408
In this paper the order and the hyper-order of the solutions of higher-order homoge-neous linear differential equations is investigated. 相似文献
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Liangwen Liao 《Journal of Mathematical Analysis and Applications》2005,309(1):91-102
We study the properties of meromorphic solutions of the Schwarzian differential equations in the complex plane by using some techniques from the study of the class Wp. We find some upper bounds of the order of meromorphic solutions for some types of the Schwarzian differential equations. We also show that there are no wandering domains nor Baker domains for meromorphic solutions of certain Schwarzian differential equations. 相似文献
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We prove a uniqueness theorem in terms of value distribution for meromorphic solutions of a class of nonlinear partial differential equations of first order, which shows that such solutions f are uniquely determined by the zeros and poles of f−cj (counting multiplicities) for two distinct complex numbers c1 and c2. 相似文献
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GaoLingyun 《高校应用数学学报(英文版)》2005,20(1):45-50
Using value distribution theory and techniques,the problem of the algebroid solutions of second order algebraic differential equation is investigated. Examples show that the results are sharp. 相似文献
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This paper is concerned with entire and meromorphic solutions of linear partial differential equations of second order with polynomial coefficients. We will characterize entire solutions for a class of partial differential equations associated with the Jacobi differential equations, and give a uniqueness theorem for their meromorphic solutions in the sense of the value distribution theory, which also applies to general linear partial differential equations of second order. The results are complemented by various examples for completeness. 相似文献
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