The doctoral dissertation in the field of Mathematics will be examined at the Faculty of Science, Forestry and Technology, Joensuu campus and online.
What is the topic of your doctoral research? Why is it important to study the topic?
My doctoral research focuses on Nevanlinna theory and delay differential equations – two classical areas within complex analysis. Nevanlinna theory has a broad range of applications, particularly in the study and solution of various equations. This thesis presents several analogues of Nevanlinna theory, along with their applications to certain delay differential equations. Specifically, we investigate an analogue of difference Nevanlinna theory. In addition, we apply Nevanlinna theory to the analysis of specific delay differential equations.
What are the key findings or observations of your doctoral research?
We began by studying two classes of delay differential equations derived from the difference Painlevé equations, using a refined approach based on Nevanlinna theory. Our results improve upon the earlier work of Halburd and Korhonen on a specific type of delay differential equation.
Finally, we introduced a variable-shift version of the analogue of the logarithmic derivative lemma in the context of difference Nevanlinna theory. In doing so, we extended the results of Asikainen, Huusko, and Korhonen by incorporating the methods developed by Chiang and Luo for handling vanishing and infinite step sizes.
What are the key research methods and materials used in your doctoral research?
At first, by incorporating singularity confinement analysis, we refined the classical Nevanlinna approach to study a more general class of delay differential equations. Finally, building on existing results and methods related to the logarithmic derivative lemma, we obtained our main results by generalizing a key lemma concerning the quotient of the difference and the derivative of a meromorphic function. In addition, several methods developed in this work are introduced here for the first time.
The doctoral dissertation of Yu Chen, MSc, entitled Value distribution theory and meromorphic solutions of certain delay differential equations will be examined at the Faculty of Science, Forestry and Technology, Joensuu Campus. The opponent will be Professor Kuldeep Singh Charak, University of Jammu, India, and the custos will be Professor Risto Korhonen, University of Eastern Finland. Language of the public defence is English.
For more information, please contact:
Yu Chen, [email protected], tel. +358 50 307 9368
