# American Institute of Mathematical Sciences

January  2019, 39(1): 503-519. doi: 10.3934/dcds.2019021

## Non-local sublinear problems: Existence, comparison, and radial symmetry

 Department of Mathematics and Informatics, via Ospedale 72, 09124 Cagliari, Italy

* Corresponding author

Received  April 2018 Revised  July 2018 Published  October 2018

We establish a symmetry result for a non-autonomous overdetermined problem associated to a sublinear fractional equation. To this purpose we prove, in particular, that the solution of the corresponding Dirichlet problem is monotonically increasing with respect to the domain. We also obtain a strong minimum principle and a boundary-point lemma for linear fractional equations that may have an independent interest.

Citation: Antonio Greco, Vincenzino Mascia. Non-local sublinear problems: Existence, comparison, and radial symmetry. Discrete & Continuous Dynamical Systems - A, 2019, 39 (1) : 503-519. doi: 10.3934/dcds.2019021
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