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

Frédéric Robert; Jérôme Vétois

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

Analysis of PDEs 2014-10-14 v2

Authors: Frédéric Robert , Jérôme Vétois

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.

Keywords

sign-changing solutions elliptic equations blowing-up solutions degenerate critical manifold glueing method analyticity nonlinear critical equations

Cite

@article{arxiv.1401.6204,
  title  = {Sign-changing solutions to elliptic second order equations: glueing a peak to a degenerate critical manifold},
  author = {Frédéric Robert and Jérôme Vétois},
  journal= {arXiv preprint arXiv:1401.6204},
  year   = {2014}
}

Comments

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

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