Graduate Student Organization Seminar

Date: September 18, 2019

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Petr Naryshkin

Title: Concentration and entire solutions to $\Delta u - u + u^3 = 0$ with various symmetries

Abstract: We introduce the notion of concentration and outline the proof of the Concentration theorem for the given variational problem. We use it to show the existence of families of entire solutions to the equation $\Delta u - u + u^3 = 0$ in $\mathbb{R}^2$ with various symmetries. We finish by extending our results to more general equations in arbitrary dimension.