Sign-changing bubble towers for asymptotically critical elliptic equations on Riemannian manifolds

Angela Pistoia (1) , Jérôme Vétois (2)

1 SBAI - Dipartimento di Scienze di Base e Applicate per l'Ingegneria
2 JAD - Laboratoire Jean Alexandre Dieudonné

Given a smooth compact Riemannian n-manifold g), we consider the equation triangle gu + hu = vertical bar u vertical bar(2*-2-epsilon)u, where h is a C-1-function on M. the exponent 2* := 2n/(n - 2) is the critical Sobolev exponent, and c is a small positive real parameter such that epsilon -> 0. We prove the existence of blowing-up families of sign-changing solutions which develop bubble towers at some point where the function h is greater than the Yamabe potential n-2/4(n-1) SCalg.

Domaines: Equations aux dérivées partielles [math.AP]

Angela Pistoia, Jérôme Vétois. Sign-changing bubble towers for asymptotically critical elliptic equations on Riemannian manifolds. Journal of Differential Equations, 2013, 254 (11), pp.4245-4278. ⟨10.1016/j.jde.2013.02.017⟩. ⟨hal-00862403⟩