@article{Peng2026, 
author = {Changwen Peng and Huawei Huang and Mengting Xia},
title = {Transcendental entire solutions of some delay differential equations},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {23050-23065},
keywords = {delay differential equation, entire solutions, Painlevé equations, Nevanlinna theory},
url = {https://www.sciopen.com/article/10.3934/math.2026929},
doi = {10.3934/math.2026929},
abstract = {The primary focus of this study was to analyze the following three delay differential equations:     ω  (  z  +  1  )  −  ω  (  z  −  1  )  +  a  (  z  )                    ω                  (          k          )                    (      z      )              ω      (      z      )        =  R  (  z  ,  ω  (  z  )  )  =            P      (      z      ,      ω      )              Q      (      z      ,      ω      )        ,     ω  (  z  +  1  )  −  ω  (  z  −  1  )  +  a  (  z  )  (                    ω        ′            (      z      )              ω      (      z      )            )    k    =  R  (  z  ,  ω  (  z  )  )  =            P      (      z      ,      ω      )              Q      (      z      ,      ω      )      and     ω  (  z  +  1  )  +  a  (  z  )                    ω                  (          k          )                    (      z      )              ω      (      z      )        =  R  (  z  ,  ω  (  z  )  )  =            P      (      z      ,      ω      )              Q      (      z      ,      ω      )        ,where    P  (  z  ,  ω  ) and    Q  (  z  ,  ω  ) were polynomials in    ω with rational coefficients in    z and no common roots,    a  (  z  ) was a rational function, and    k  ≥  1 was an integer. This paper investigated the forms of the transcendental entire solutions for the above equations. Some examples were given to support these results.}
}