Sign-changing solutions to elliptic second order equations: glueing a peak to a degenerate critical manifold

2014/01/23 by Frédéric Robert, Jérôme Vétois, Robert, Frédéric +1 · 1 citation
Computer Science · Mathematics · #35B44 #35J35 #35J60 #58J05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.AP #msc:35B44 #msc:35J35 #msc:35J60 #msc:58J05

paper · pdf · doi:10.48550/arxiv.1401.6204

Final version to appear in "Calculus of Variations and PDEs"

openalex publication_date 2014/01/23 · arxiv created 2014/10/13 · arxiv updated 2014/10/14 · openalex created_date 2022/08/05 · openalex updated_date 2026/07/28

Abstract

We construct blowing-up sign-changing solutions to some nonlinear critical equations by glueing a standard bubble to a degenerate function. We develop a method based on analyticity to perform the glueing when the critical manifold of solutions is degenerate and no Bianchi--Egnell type condition holds.

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• Ground-state blowing-up solutions for a Hardy-Sobolev equations on a manifold

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