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On the bubbling solutions of the Maxwell-Chern-Simons model on flat torus. Ao, Weiwei


We consider the periodic solutions of a nonlinear elliptic system derived from the Maxwell-Chern-Simons model on a flat torus $\Omega$: $$\left\{\begin{array}{l} \Delta u=\mu(\lambda e^u-N)+4\pi\sum_{i=1}^n m_{i}\delta_{p_i},\\ \Delta N=\mu (\mu+\lambda e^u)N-\lambda \mu(\lambda+\mu)e^u \end{array} \right. \mbox{ in }\Omega, $$ where $\lambda, \mu>0$ are positive parameters. We obtain a Brezis-Merle type classification result for this system when $\lambda, \mu \to \infty$ and $\lambda<<\mu$. We also construct blow up solutions to this system. This is a joint work with Youngae Lee and Kwon Ohsang.

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