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A remark on existence and optimal summability of solutions of elliptic problems involving Hardy potential
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 |
$ -\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.
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