Growth of meromorphic solutions of delay differential equations

TL;DR

This paper establishes necessary conditions for rational delay differential equations to have non-rational meromorphic solutions with hyper-order less than one, including delay Painlevé and elliptic function equations.

Contribution

It provides new criteria for the existence of low hyper-order meromorphic solutions in specific delay differential equations.

Findings

Identifies conditions for meromorphic solutions with hyper-order less than one.

Includes delay Painlevé equations and elliptic function solutions.

Advances understanding of solution growth in delay differential equations.

Abstract

Necessary conditions are obtained for certain types of rational delay differential equations to admit a non-rational meromorphic solution of hyper-order less than one. The equations obtained include delay Painlev\'e equations and equations solved by elliptic functions.