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Session S22 - Deterministic and probabilistic aspects of nonlinear evolution equations

Friday, July 16, 16:00 ~ 16:30 UTC-3

On the uniqueness of excited states of semilinear evolution equations.

Wilhelm Schlag

Yale University, United States of America   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We will discuss the problem of existence and uniqueness of nonzero solutions of finite energy to semilinear elliptic PDEs, which characterize stationary solutions of nonlinear evolution equations. The uniqueness question, which is often delicate, has consequences for the spectral properties of the linearized operators. This in turn is of essence for the long-term dynamics of solutions. In particular, I will describe recent work with Alex Cohen and Kevin Li at Yale on the uniqueness of the first few excited states for the cubic problem in three dimensions.

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