Proceedings of the Japan Academy, Series A, Mathematical Sciences

On analogies between nonlinear difference and differential equations

Chung-Chun Yang and Ilpo Laine

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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

Permanent link to this document
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

Subjects
Primary: 39B32: Equations for complex functions [See also 30D05] 34M05: Entire and meromorphic solutions 30D35: Distribution of values, Nevanlinna theory

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

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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References

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