Hostname: page-component-7bb8b95d7b-w7rtg Total loading time: 0 Render date: 2024-10-06T03:47:11.178Z Has data issue: false hasContentIssue false
  • English
  • Français

A rigidity result for non-local semilinear equations

Part of: Partial differential equations Miscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  31 May 2017

Alberto Farina  and
Enrico Valdinoci
Alberto Farina
Affiliation:
Department of Mathematics and Statistics, University of Melbourne, Parkville, VIC 3010, Australia and Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117 Berlin, Germany and Dipartimento di Matematica, Università degli Studi di Milano, Via Cesare Saldini 50, 20133 Milano, Italy (enrico@math.utexas.edu)
Enrico Valdinoci
Affiliation:
Department of Mathematics and Statistics, University of Melbourne, Parkville, VIC 3010, Australia and Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117 Berlin, Germany and Dipartimento di Matematica, Università degli Studi di Milano, Via Cesare Saldini 50, 20133 Milano, Italy (enrico@math.utexas.edu)
Get access Rights & Permissions [Opens in a new window]

Extract

We consider a possibly anisotropic integrodifferential semilinear equation, driven by a non-decreasing nonlinearity. We prove that if the solution grows less than the order of the operator at infinity, then it must be affine (possibly constant).

Keywords

non-local integrodifferential semilinear equationsLiouville-type theoremsnon-decreasing nonlinearities

MSC classification

Secondary: 35R11: Fractional partial differential equations 35B53: Liouville theorems, Phragmén-Lindelöf theorems 35R09: Integro-partial differential equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 147 , Issue 5 , October 2017 , pp. 1009 - 1018
Copyright
Copyright © Royal Society of Edinburgh 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)