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

Frédéric Robert (1) , Jérôme Vétois (2)

1 IECL - Institut Élie Cartan de Lorraine
2 LJAD - Laboratoire Jean Alexandre Dieudonné

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.

Domaines: Equations aux dérivées partielles [math.AP]

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, 2015, 54 (1), pp.693-716. ⟨10.1007/s00526-014-0802-1⟩. ⟨hal-01097282⟩