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


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, u H1(N) N 3, where λ 0, 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.