PDE Seminar Abstracts

Huan-Song Zhou

Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan

26 Oct 2009 3-4pm, Carslaw Room 454

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 SchrÃ¶dinger equation: $-\Delta u+\left(1+\lambda g\left(x\right)\right)u=f\left(u\right)$ and $u>0$ in ${\mathbb{R}}^{N}$, $u\in {H}^{1}\left({\mathbb{R}}^{N}\right)$ $N\ge 3$, where $\lambda \ge 0$, $g\left(x\right)\in {L}^{\infty}\left({\mathbb{R}}^{N}\right)$ which vanishes on a bounded domain in ${\mathbb{R}}^{N}$, and $f\left(s\right)~\left(\alpha +1\right)s$ at $+\infty $. We discuss how the existence and behavior of the solutions of the equation depend on the parameters $\lambda $ and $\alpha $. This is joint work with C.A.Stuart and Z.P. Wang.

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