Article Contents
Article Contents

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

• 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.

Mathematics Subject Classification: Primary: 35J25, 35J20; Secondary: 35B33.

 Citation: