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$-\Delta u + e^u - e^{-u} = \delta(\vec{x})$, where $\Delta$ is the Laplace operator and $\delta(\vec{x})$ is the Dirac's delta function and satisfies: $\delta(\vec{x}) = \begin{cases} 0, & \vec{x} \neq \vec{0} \\ \infty & \vec{x} = \vec{0} \end{cases}$ and $ \int_{R^2} f(\vec{x})\delta(\vec{x}) \,d\vec{x} = f(\vec{0})$ where $f$ is any bounded and continuous function in $\mathbb{R}^2$.

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