**SMS scnews item created by Daniel Daners at Wed 21 Oct 2009 0936**

Type: Seminar

Modified: Wed 21 Oct 2009 0937; Fri 23 Oct 2009 1322

Distribution: World

Expiry: 26 Oct 2009

**Calendar1: 26 Oct 2009 1500-1600**

**CalLoc1: Carslaw 454**

Auth: daners@p7153.pc.maths.usyd.edu.au

### PDE Seminar

# On the existence of stationary solutions of nonlinear Schrödinger equations

### Zhou

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},
u H^{1}(^{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.

Check also the PDE Seminar page. Enquiries to Florica Cîrstea or Daniel Daners.