2023/01/10 by Tingbin Cao, Yu Chen, Risto Korhonen · 2 citations
Mathematics · #Advanced Differential Equations and Dynamical Systems #Meromorphic and Entire Functions
paper · doi:10.1016/j.bulsci.2023.103227
openalex publication_date 2023/01/10 · crossref created 2023/01/10 · crossref issued 2023/02/01 · crossref published 2023/02/01 · crossref published-print 2023/02/01 · crossref deposited 2025/09/13 · openalex created_date 2025/10/10 · crossref indexed 2026/07/30 · openalex updated_date 2026/07/30
We study the higher order delay differential equationsw(z+1)−w(z−1)+a(z)w(k)(z)w(z)=R(z,w(z)), andw(z+1)+a(z)w(k)(z)w(z)=R(z,w(z)), where k is a positive integer, a(z) is a rational function and R(z,w) is rational in w with rational coefficients. We obtain necessary conditions on the degree of R(z,w) for these delay differential equations to admit a subnormal transcendental meromorphic solution. These results generalize some of the previous results by Halburd and Korhonen (2017) [7] to higher order case. Some examples are given to support our conclusions.