Nodal bubble-tower solutions to radial elliptic problems near criticality

Contreras, A; Del Pino M.

Abstract

We describe as ε → 0 radially symmetric sign-changing solutions to the problem -Δu = |u|4/N - 2 - ε u in B where B is the unit ball in ℝN, N ≥ 3, under zero Dirichlet boundary conditions. We construct radial solutions with k nodal regions which resemble a superposition of "bubbles" of different signs and blow-up orders, concentrating around the origin. A dual phenomenon is described for the slightly supercritical problem -Δu = |u|4/N - 2 + ε u in ℝN \ B under Dirichlet and fast vanishing-at-infinity conditions.

Más información

Título según WOS: Nodal bubble-tower solutions to radial elliptic problems near criticality
Título según SCOPUS: Nodal bubble-tower solutions to radial elliptic problems near criticality
Título de la Revista: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
Volumen: 16
Número: 3
Editorial: AMER INST MATHEMATICAL SCIENCES-AIMS
Fecha de publicación: 2006
Página de inicio: 525
Página final: 539
Idioma: English
Notas: ISI, SCOPUS