PDE Seminar Abstracts

On the existence of stationary solutions of nonlinear Schrödinger equations

Huan-Song Zhou
Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan
26 Oct 2009 3-4pm, Carslaw Room 454

Abstract

In this talk, we will talk about the following type of nonlinear stationary Schrödinger equation: -Δu+(1+λg(x))u=f(u) and u>0 in N, uH1(N) N3, where λ0, g(x)L(N) which vanishes on a bounded domain in N, and f(s)~(α+1)s at +. We discuss how the existence and behavior of the solutions of the equation depend on the parameters λ and α. This is joint work with C.A.Stuart and Z.P. Wang.