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arXiv · 1306.1274

Regular solutions to a supercritical elliptic problem in exterior domains

Juan Dávila·Luis F. López
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Abstract

We consider the supercritical elliptic problem -\Delta u = \lambda e^u, \lambda > 0, in an exterior domain $\Omega = \mathbb{R}^N \setminus D$ under zero Dirichlet condition, where D is smooth and bounded in \mathbb{R}^N, N greater or equal than 3. We prove that, for \lambda small, this problem admits infinitely many regular solutions.

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Juan Dávila, Luis F. López. 2013-06-06. Regular solutions to a supercritical elliptic problem in exterior domains. https://doi.org/10.1016/j.jde.2013.04.024

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