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

Antonio Greco; Vincenzino Mascia

doi:10.3934/dcds.2019021

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2019, Volume 39, Issue 1: 503-519. Doi: 10.3934/dcds.2019021

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

Antonio Greco^, and
Vincenzino Mascia

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

* Corresponding author
* Corresponding author

Received: April 2018

Revised: July 2018

Published: January 2019

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Abstract

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.

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Mathematics Subject Classification: Primary: 35N25; Secondary: 35B51, 35S15.

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References

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