Positive solutions to the sublinear Lane-Emden equation are isolated
Analysis of PDEs
2019-11-22 v1
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 eigenvalue of the Dirichlet-Laplacian is not an accumulation point of the spectrum, on a smooth bounded set. Our results extend to a suitable class of Lipschitz domains, as well.
Keywords
Cite
@article{arxiv.1911.09163,
title = {Positive solutions to the sublinear Lane-Emden equation are isolated},
author = {Lorenzo Brasco and Guido De Philippis and Giovanni Franzina},
journal= {arXiv preprint arXiv:1911.09163},
year = {2019}
}