Meromorphic solutions of higher order delay differential equations

Abstract

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.