037 Risto Korhonen

Delay differential equations and Nevanlinna theory // The idea that the existence of sufficiently many finite-order meromorphic solutions could be used to single out difference Painlevé equations was introduced by Ablowitz, Halburd and Herbst. In this talk necessary conditions are obtained for certain types of delay differential equations to admit a transcendental meromorphic solution of hyper-order less than one. The equations obtained include delay Painlevé equations and equations solvable by elliptic functions. We conclude with recent results on the existence of transcendental meromorphic solutions of first-order difference equations, without growth conditions.