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arXiv · 1911.09163

Positive solutions to the sublinear Lane-Emden equation are isolated

Lorenzo Brasco·Guido De Philippis·Giovanni Franzina
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Abstract

We prove that on a smooth bounded set, the positive least energy solution of the Lane-Emden equation with sublinear power is isolated. As a corollary, we obtain that the first $q-$eigenvalue of the Dirichlet-Laplacian is not an accumulation point of the $q-$spectrum, on a smooth bounded set. Our results extend to a suitable class of Lipschitz domains, as well.

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Lorenzo Brasco, Guido De Philippis, Giovanni Franzina. 2019-11-20. Positive solutions to the sublinear Lane-Emden equation are isolated. https://arxiv.org/abs/1911.09163

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