In this short course I will introduce some elements of bifurcation theory, such as the Lyapunov-Schmidt reduction, the bifurcation from the simple eigenvalue, and the Krasnoselski bifurcation theorem. Then, I will discuss some applications to the theory of MFG systems: existence of periodic in time solutions, and multi-population problems.
Marco Cirant is an assistant professor at the University of Padova. He received his Ph.D. in Mathematics from the University of Padova in 2014, and he did his Post-Doc at the University of Milano. Then, he has been assistant professor at the University of Parma in 2019. Cirant’s research interests are in partial differential equations, in particular in semi-linear and fully-nonlinear elliptic PDEs and systems arising in Mean-Field Games models