Entire solutions of a class of delay-differential equations

Changwen Peng^a, Zhijin Zhou^a, Huawei Huang^b,*, Lei Tao^c

ABSTRACT: This study focuses on the delay-differential equation ?gg +B(z)g?/g = R(z, g) = P(z,g) Q(z,g) , where P(z, g) and Q(z, g) are polynomials in g with rational coefficients in z and no common roots, B(z) is rational and g ? g(z), ?g ? g(z +1), g ? g(z?1). Reduced forms of this equation arise when it admits a transcendental entire solution of hyper order less than one. Furthermore, we examine the properties of entire solutions for these reduced forms.

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^a	School of Science, Guiyang University, Guiyang 550005 China
^b	School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025 China
^c	School of Mathematics and Big Data, Guizhou Education University, Guiyang 550018 China

* Corresponding author, E-mail: hwhuang7809@163.com

Received 7 Aug 2025, Accepted 9 Aug 2026

Entire solutions of a class of delay-differential equations

Changwen Penga, Zhijin Zhoua, Huawei Huangb,*, Lei Taoc

Changwen Peng^a, Zhijin Zhou^a, Huawei Huang^b,*, Lei Tao^c