Proceedings of the Japan Academy, Series A, Mathematical Sciences

On analogies between nonlinear difference and differential equations

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.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 86, Number 1 (2010), 10-14.

Dates
First available in Project Euclid: 31 December 2009

https://projecteuclid.org/euclid.pja/1262271517

Digital Object Identifier
doi:10.3792/pjaa.86.10

Mathematical Reviews number (MathSciNet)
MR2598818

Zentralblatt MATH identifier
1207.34118

Citation

Yang, Chung-Chun; Laine, Ilpo. On analogies between nonlinear difference and differential equations. Proc. Japan Acad. Ser. A Math. Sci. 86 (2010), no. 1, 10--14. doi:10.3792/pjaa.86.10. https://projecteuclid.org/euclid.pja/1262271517

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