The doctoral dissertation in the field of聽Mathematics,聽will be examined at the Faculty of Science, Forestry and Technology, Joensuu campus.
What is the topic of your doctoral research? Why is it important to study the topic?
The topic of my doctoral research focuses on the study of meromorphic solutions of delay differential equations and on analytic solutions of difference equations. The research focuses on differences and delays of differential equations, an area experiencing rapid development. The dissertation presents original theorems on delay differential equations under the assumption that there exists a meromorphic solution with hyper-order less than one 鈥 a condition closely related to the integrability of the equation. These results therefore contribute significant new insights to the field.
What are the key findings or observations of your doctoral research?
The dissertation presents a series of theorems that contribute to the understanding of delay differential and difference equations. Theorem 5.1 examines the relationship between the degrees of polynomials and the growth of solutions in delay differential equations. Theorem 5.2 extends this analysis to equations where the right-hand side is independent of the unknown function w. Theorem 5.3 generalizes earlier results to include rational functions, while Theorem 5.4 explores the impact of higher powers of w in the denominator of previously studied equations. Theorem 5.5 investigates the existence and degree conditions for non-rational meromorphic solutions, offering a detailed case analysis based on the degrees of the polynomials P (z, w), Q (z, w), and R (z, w). Theorem 5.6 addresses a more intricate equation involving interactions between terms in both the numerator and denominator, providing a structural analysis of the solution behavior. In the context of difference equations, Theorem 5.7 proves the existence of meromorphic solutions to certain nonlinear equations, outlining specific conditions for their existence and behavior. Theorem 5.8 establishes the uniqueness of meromorphic solutions for equations with meromorphic coefficients under given constraints. Finally, Theorem 5.9 presents additional results concerning analytic solutions within specified domains.
What are the key research methods and materials used in your doctoral research?
The proofs involve a variety of advanced methods not only from classical value distribution theory and more recent differences in Nevanlinna theory, but also more general analytic methods. The mathematical content of the dissertation is presented in an orderly manner, proceeding from basic information on Nevanlinna theory, through more recent and specific results forming foundation and inspiration of my original research, to finally present the original results.
The doctoral dissertation of Yan Liu, MSc, entitled Studies on meromorphic solutions of delay differential equations and on analytic solutions of difference equations will be examined at the Faculty of Science, Forestry and Technology, Joensuu Campus. The opponent will be Associate Professor Zinelaabidine Latreuch, Sultan Qaboos University, Sultanate of Oman, and the custos will be Docent Janne Heittokangas, 91天美. Language of the public defence is English.
For more information, please contact:
Yan Liu, liuyan@student.uef.fi, tel. 041 811 7560
- Public examination
- (PDF)
