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| We present recent results on finite energy solutions $A:\Omega\to\mathbb{R}^3$ of the equation
$$ \nabla\times(\nabla\times A) + V(x) A = \partial_Af(x,A) $$
on a smooth bounded domain $\Omega$ of $\mathbb{R}^3$ with boundary condition $n\times A=0$ on $\partial\Omega$. Here "$\nabla\times$" denotes the curl operator, $V\in L^\infty_{loc}(\Omega)$ is bounded below, and $f: \Omega\times\mathbb{R}^3\to\mathbb{R}$ is a superlinear and subcritical nonlinearity; $n$ is the exterior normal to the boundary. |
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