Conferenciante: Peter Polacik, University of Minnesota

Fecha: Miércoles 23 de febrero de 2022 - 15:00

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Resumen: We consider positive solutions of nonlinear elliptic equations on the (N+1)-dimensional Euclidean space with some predetermined behavior (such as decay and symmetry) in the first N variables. We examine the behavior of these solutions in the remaining variable. Families of solutions periodic in the last variable have been found by several authors; our goal is to prove the existence of quasiperiodic solutions. For this purpose, we examine the spatial dynamics of the equation on a center manifold and apply KAM-type results. In the lecture, I will outline our general techniques and report on recent progress. This is joint work with Dario Valdebenito.