Usted está aquí: Vortex–Type Solutions to a Magnetic Nonlinear Choquard Equation

# Vortex–Type Solutions to a Magnetic Nonlinear Choquard Equation

Ponente: Dora Salazar
Cuándo 20/11/2014 de 11:00 a 12:00 Salón de seminarios Graciela Salicrup vCal iCal

We consider the stationary nonlinear magnetic Choquard equation
\begin{equation*}
(-\mathrm{i}\nabla+A(x))^2u+W(x)u=\left(\frac{1}{|x|^\alpha}*|u|^p\right)
\end{equation*}
where $$N\ge 3$$, $$\alpha\in(0,N)$$,
$$p\in\left[2,\frac{2N-\alpha}{N-2}\right)$$,
$$A\colon\mathbb{R}^N\to\mathbb{R}^N$$ is a magnetic potential and
$$W\colon\mathbb{R}^N\to\mathbb{R}$$ is a bounded electric potential. We
assume that both $$A$$ and $$W$$ are compatible with the action of some
group $$\Gamma$$ of linear isometries of $$\mathbb{R}^N$$.

We shall give an overview and present some recent results concerning the
existence of vortex-type solutions to this equation which satisfy the symmetry
condition
\begin{equation*}
u(\gamma x)=\phi(\gamma)u(x)
where $$\phi\colon\Gamma\to\mathbb{S}^1$$ is a given continuous group