# American Institute of Mathematical Sciences

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September  2006, 16(3): 525-539. doi: 10.3934/dcds.2006.16.525

## Nodal bubble-tower solutions to radial elliptic problems near criticality

 1 Departamento de Ingeniería Matemática, Universidad de Chile, Casilla 170, Correo 3, Santiago, Chile, Chile

Received  February 2006 Revised  June 2006 Published  August 2006

We describe as $\varepsilon \to 0$ radially symmetric sign-changing solutions to the problem

$-\Delta u =|u|^{\frac 4{N-2} -\varepsilon} u \quad \text{in } B$

where $B$ is the unit ball in $\R^N$, $N\ge 3$, 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

$-\Delta u =|u|^{\frac 4{N-2} +\varepsilon} u \quad \text{in } \R^N \setminus B$

under Dirichlet and fast vanishing-at-infinity conditions.

Citation: Andrés Contreras, Manuel del Pino. Nodal bubble-tower solutions to radial elliptic problems near criticality. Discrete & Continuous Dynamical Systems - A, 2006, 16 (3) : 525-539. doi: 10.3934/dcds.2006.16.525
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