Minicourse by Csaba Farkas at Corvinus
The professor of the Sapientia Hungarian University of Transylvania will give a lecture on “Introduction to the theory of critical points with applications”.
Date: 16 September 9:50 – 17 September 15:10
Location: Corvinus University, Building C
The Corvinus Centre for Operations Research (CCOR), the Corvinus Institute of Advanced Studies (CIAS), and the Institute of Operations and Decision Sciences invite you to the minicourse by Professor Csaba Farkas (Sapientia Hungarian University of Transylvania).
Dates:
September 16. (Monday) 9:50-11:20 (Room C418)
September 17. (Tuesday) 9:50-11:20 (Room C103)
September 17. (Tuesday) 13:40-15:10 (Room C101)
We would like to inform you that the lectures will be broadcast online. Please be aware that this broadcast will not utilize professional-grade equipment, and we appreciate your understanding that we cannot ensure the broadcast’s quality.
If you would like to join online, please send an e-mail to petra.rigo@uni-corvinus.hu by September 15.
Abstract of the topic
Variational and topological methods have proven to be powerful tools for solving concrete nonlinear boundary value problems across various disciplines, particularly where classical methods might fail. This is especially true for critical point theory, which has gained significant traction in recent years. Its success can be attributed not only to its theoretical elegance but also to the wide range of problems it can effectively address.
In this series of three lectures, we will be introduced to the fundamentals of the calculus of variations and critical point theory. We will begin by exploring the basics of the calculus of variations, focusing specifically on the Euler-Lagrange equations and their applications. Following this, we will discuss the one-dimensional Mountain Pass Theorem (MPT) and introduce Courant’s finite-dimensional version. Additionally, we will present Ekeland’s variational principle along with several of its applications. Using Ekeland’s variational principle, we will also establish the infinite-dimensional MPT developed by Ambrosetti and Rabinowitz. Finally, we will examine some applications of the MPT, particularly demonstrating the existence of weak solutions to the semi-linear Dirichlet problem, as well as exploring certain applications in game theory.
We welcome you to the event!