A mean field equation with symmetry on torus

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让 T 2 是有基本房间领域 $\\left 的一个完全二维的花托[{- \\tfrac { 1 }{ 2 }, \\tfrac { 1 }{ 2 }} \\right ] \\times \\left [{- \\tfrac { 1 }{ 2 }, \\tfrac { 1 }{ 2 }} \\right ] $\\left [{- \\tfrac { 1 }{ 2 }, \\tfrac { 1 }{ 2 }} \\right ] \\times \\left [{- \\tfrac { 1 }{ 2
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