Stable solutions of -Δu = f(u) in \R^N

2008/06/03 by Louis Dupaigne, Alberto Farina, Dupaigne, Louis +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.0806.0492

openalex publication_date 2008/06/03 · arxiv created 2008/06/17 · arxiv updated 2009/12/01 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

The paper proves Liouville-type results for stable solutions of semilinear elliptic PDEs with convex nonlinearity, posed on the entire Euclidean space. Extensions to solutions which are stable outside a compact set are also presented.

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