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Results tagged with elliptic-pde
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user 108518
Questions about partial differential equations of elliptic type. Often used in combination with the top-level tag ap.analysis-of-pdes.
1
vote
0
answers
44
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Uniqueness of positive solutions to the n-vortex type equation
The $n$-vortex equation, in the context of optical vortex solitons, is of the form
\begin{equation}
-(ru_{r})_r+\dfrac{n^2}{r}u+\beta ru= f(u^2)ru,\quad r\in (0,\infty),\\
u(0)=0=u(\infty),
\end{equa …
3
votes
1
answer
164
views
Is this space compactly contained in $L^p((0,\infty),rdr)$ for all $p\geq 2$?
Some Background: A typical problem in mathematical physics is the existence of positive radially symmetric solutions to a nonlinear Schrodinger type equation over $\mathbb{R}^{2+1}$. Such a problem ty …