Speaker: Zhang Meirong, Professor and Doctoral Supervisor, Department of Mathematical Sciences, Tsinghua University

Inviter: Hu Xijun, Professor of School of Mathematics, Shandong University

Date: Apr.23, 2021

Time: 3:00-4:00p.m.

Location: Lecture Hall 1248, Block B, Zhixin Building, Central Campus

Abstract:

The periodic eigenvalue problem resultsfrom the variational treatment to the critical points of the p-th kinetic energy under the constant constraint to p-th potential energy of periodic motions in the Euclidean spaces Rd. This is a Euler-Lagrangian equation on Rd. In dimension d=2, it has been known that the problem admits two different sequences of eigenvalues. A problem proposed by Manásevich and Mawhin 20 years ago is that if these are all periodic eigenvalues.

In this talk, I will show that for any exponent p≠2, the p-Laplacian on the plane will actually admit infinitely many different sequences of periodic eigenvalues. They are constructed using a notion of scaling angular momenta we will introduce. The whole proof is based on: (1) the complete integrability of the equivalent Hamiltonian system, (2) a tricky reduction to 2-dimensional dynamical systems, and (3) a number-theoretical distinguishing between different sequences of eigenvalues.

Some numerical simulations and further problems will be given.

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/149409.htm