A Liouville theorem for the fractional Ginzburg-Landau equation

In this paper, we are concerned with a Liouville-type result of the nonlinear integral equation \begin{equation*} u(x)=\int_{\mathbb{R}^{n}}\frac{u(1-|u|^{2})}{|x-y|^{n-\alpha}}dy, \end{equation*} where $u: \mathbb{R}^{n} \to \mathbb{R}^{k}$ with $k \geq 1$ and $1<\alpha

Keywords:

• Mathematics
• nonlinear integral equation
• Differentiable function
• Liouville's theorem (Hamiltonian)
• Bounded function
• ginzburg landau equation
• Mathematical analysis
• Mathematical physics

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