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.