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

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 new 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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Submitted on : Friday, December 19, 2014 - 12:42:38 PM
Last modification on : Tuesday, March 2, 2021 - 5:12:05 PM
Long-term archiving on: : Monday, March 23, 2015 - 5:45:42 PM

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Frédéric Robert, Jérôme Vétois. Sign-changing solutions to elliptic second order equations: glueing a peak to a degenerate critical manifold. Calculus of Variations and Partial Differential Equations, Springer Verlag, 2015, 54 (1), pp.693-716. ⟨10.1007/s00526-014-0802-1⟩. ⟨hal-01097282⟩

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