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

作　　者：Mingyue Wu Mingyue Wu(School of Science, Beijing University of Posts and Telecommunications, Beijing, China;Key Laboratory of Mathematics and Information Networks (Beijing University of Posts and Telecommunications), Ministry of Education, Beijing, China)

机构地区：[1]School of Science, Beijing University of Posts and Telecommunications, Beijing, China [2]Key Laboratory of Mathematics and Information Networks (Beijing University of Posts and Telecommunications), Ministry of Education, Beijing, China

出　　处：《Open Journal of Applied Sciences》2023年第12期2329-2342,共14页应用科学(英文)

摘　　要：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.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.

关 键 词：Non-Linear Delay Differential Equations Painlevé Type Equations Nevanlinna Theory Meromorphic Function Solutions Minimal Hypertype 

分 类 号：O17[理学—数学]