CSH Talk by Jelena Manojlovic “Karamata Theory of regular variation and asymptotic analysis of nonlinear differential equations”

Jelena Manojlovic (University of Nis) will present a talk on Thursday, June 22nd, 2023 at 3 PM in Room 201.

Title: Karamata Theory of regular variation and asymptotic analysis of nonlinear differential equations

Abstract: The lecture will first present the essential elements of Karamata’s theory of regularly varying functions, and then give an overview of the results obtained over the past years in the application of this theory in the asymptotic analysis of positive solutions of second-order differential equations  A classification of positive solutions will be performed and it will be shown that all positive increasing and all positive decreasing solutions of the equation are regularly varying or rapidly varying, under the assumption that the coefficient of the equation is a regularly varying or rapidly varying function. It will be shown that by applying Karamata’s theory it is possible to obtain not only complete information about the existence of solutions that belong to all possible classes of positive solutions obtained by classification (in the sense of determining the necessary and sufficient conditions for existence), but it is also possible to explicitly determine the appropriate asymptotic representations of all types of regularly and rapidly varying solutions.

Bio: Jelena Manojlović is a full professor at the University of Niš, Faculty of Science and Mathematics since 2009 and received her Ph.D. in Mathematics at the University of Belgrade in 2000. Her main research interest is the Qualitative theory of nonlinear differential and difference equations within which her research is dedicated to an asymptotic analysis of nonlinear differential and nonlinear difference equations, the theory of regular variation and differential equations, the q-calculus and the asymptotic analysis of nonlinear q-difference equations and the applied bifurcation theory. Jelena has published about 60 research articles and participated in more than 30 International Conferences. She was a Matsumae International Foundation fellowship from October 2004 to April 2005 at Fukuoka University, Japan. Also, she was a visiting professor and invited lecture speaker at more than ten universities.