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Ablowitz, M.J., Halburd, R. and Herbst, B. (2000) On the Extension of the Painlevé Property to Difference Equations. Nonlinearity, 13, 889.
https://doi.org/10.1088/0951-7715/13/3/321

has been cited by the following article:

• TITLE: The Existence of Meromorphic Solutions to Non-Linear Delay Differential Equations

  AUTHORS: Mingyue Wu

  KEYWORDS: Non-Linear Delay Differential Equations, Painlevé Type Equations, Nevanlinna Theory, Meromorphic Function Solutions, Minimal Hypertype

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.13 No.12, December 20, 2023

  ABSTRACT: In this paper, we study the existence of the transcendental meromorphic solution of the delay differential equations , where a(z)is a rational function,andare polynomials in w(z)with rational coefficients, k is a positive integer. Under the assumption when above equations own transcendental meromorphic solutions with minimal hyper-type, we derive the concrete conditions on the degree of the right side of them. Specially, when w(z)=0 is a root of, its multiplicity is at most k. Some examples are given here to illustrate that our results are accurate.