The Existence of Meromorphic Solutions to Non-Linear Delay Differential Equations - Open Journal of Applied Sciences

OJAppS > Vol.13 No.12, December 2023

Open Journal of Applied Sciences

Volume 13, Issue 12 (December 2023)

ISSN Print: 2165-3917 ISSN Online: 2165-3925

Google-based Impact Factor: 1 Citations

The Existence of Meromorphic Solutions to Non-Linear Delay Differential Equations ()

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Download as PDF (Size: 453KB) PP. 2329-2342

DOI: 10.4236/ojapps.2023.1312182 103 Downloads 361 Views

Author(s)

Mingyue Wu^1,2

Affiliation(s)

¹School of Science, Beijing University of Posts and Telecommunications, Beijing, China.
²Key Laboratory of Mathematics and Information Networks (Beijing University of Posts and Telecommunications), Ministry of Education, Beijing, China.

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,

and

are 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.

KEYWORDS

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

Share and Cite:

Wu, M. (2023) The Existence of Meromorphic Solutions to Non-Linear Delay Differential Equations. Open Journal of Applied Sciences, 13, 2329-2342. doi: 10.4236/ojapps.2023.1312182.

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