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arXiv · 1703.10388

The Fredholm alternative for the $p$-Laplacian in exterior domains

Pavel Drabek·Ky Ho·Abhishek Sarkar
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Abstract

We investigate the Fredholm alternative for the $p$-Laplacian in an exterior domain which is the complement of the closed unit ball in $\mathbb{R}^N$ ($N\geq 2$). By employing techniques of Calculus of Variations we obtain the multiplicity of solutions. The striking difference between our case and the entire space case is also discussed.

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Pavel Drabek, Ky Ho, Abhishek Sarkar. 2017-03-30. The Fredholm alternative for the $p$-Laplacian in exterior domains. https://arxiv.org/abs/1703.10388

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