School of Mathematical Sciences Academic Report [2023] No. 064

(High-level University Construction Series Report No. 835)

Report title: Existence of subpure solutions of first order difference equations

Speaker: Yueyang Zhang (University of Science and Technology Beijing)

Reporting time: October 07, 2023, 15:00-16:00

Location: Room 701, Zhi Zhi Building

Report Content: The classical Malmquist theorem states that if a first-order nonlinear differential equation f'(z)=R(z,f) has a transcendental subpure solution, where R(z,f) is rational with respect to z and f, then this equation must degenerate to the Riccati equation. This result has been generalized by scholars to the higher case f'(z)^n=R(z,f). This report focuses on the existence of subpure solutions of first-order difference equations f(z+1)^n=R(z,f) and how to find all subpure solutions of such equations, including elliptic function solutions, exponential function solutions, and so on. The main tool used to solve such first-order difference equations is Nevanlinna theory. Some recent advances on the solution of first-order q-difference equations are also presented, among others.

Reporter Introduction:Yueyang Zhang is a lecturer in the School of Mathematics and Science, University of Science and Technology Beijing.He graduated from Beijing University of Aeronautics and Astronautics with a Doctor of Science degree (in the direction of complex analysis in basic mathematics) in 2018.He visited the University of Eastern Finland, Finland, and the University College London, UK, successively funded by the National Foundation for International Students and is a commentator of the American Mathematical Review. He is mainly engaged in academic research on complex analysis and its applications. He has published dozens of papers in national and international SCI journals, such as Constr. Approx., Ann. Acad. Sci. Fenn. Ser. A, and JMAA. Recently, his main research interests are Nevanlinna theory and its applications to differential equations and difference equations. Currently, he is the chair of the Basic Research Funds of Universities and the Youth Fund of the National Natural Science Foundation of China.

Teachers and students are welcome to participate!

Inviter: Huang Jiaxing

School of Mathematical Sciences

October 07, 2023