Vol. 15, No. 2, 2022

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Classification and Liouville-type theorems for semilinear elliptic equations in unbounded domains

Louis Dupaigne and Alberto Farina

Vol. 15 (2022), No. 2, 551–566
Abstract

We classify stable and finite Morse index solutions to general semilinear elliptic equations posed in Euclidean space of dimension at most 10 and in some unbounded domains of dimension at most 11.

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Keywords
semilinear elliptic PDEs, Liouville-type theorems, stable solutions
Mathematical Subject Classification
Primary: 35J15
Milestones
Received: 25 May 2020
Revised: 3 August 2020
Accepted: 6 October 2020
Published: 12 April 2022
Authors
Louis Dupaigne
Institut Camille Jordan
UMR CNRS 5208
Université Claude Bernard Lyon 1
Villeurbanne
France
Alberto Farina
LAMFA, UMR CNRS 7352
Université Picardie Jules Verne
Amiens
France