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January 2010 On analogies between nonlinear difference and differential equations
Chung-Chun Yang, Ilpo Laine
Proc. Japan Acad. Ser. A Math. Sci. 86(1): 10-14 (January 2010). DOI: 10.3792/pjaa.86.10

Abstract

In this paper, we point out some similarities between results on the existence and uniqueness of finite order entire solutions of the nonlinear differential equations and differential-difference equations of the form $$f^n+L(z,f)=h.$$ Here n is an integer $\geq 2$, h is a given non-vanishing meromorphic function of finite order, and L(z,f) is a linear differential-difference polynomial, with small meromorphic functions as the coefficients.

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Chung-Chun Yang. Ilpo Laine. "On analogies between nonlinear difference and differential equations." Proc. Japan Acad. Ser. A Math. Sci. 86 (1) 10 - 14, January 2010. https://doi.org/10.3792/pjaa.86.10

Information

Published: January 2010
First available in Project Euclid: 31 December 2009

zbMATH: 1207.34118
MathSciNet: MR2598818
Digital Object Identifier: 10.3792/pjaa.86.10

Subjects:
Primary: 30D35 , 34M05 , 39B32

Keywords: difference polynomial , difference-differential equation , Difference-differential polynomial , Nevanlinna theory

Rights: Copyright © 2010 The Japan Academy

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Vol.86 • No. 1 • January 2010
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