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MULTI-BUBBLE SOLUTIONS FOR SLIGHTLY SUPER-CRITICAL ELLIPTIC PROBLEMS IN DOMAINS WITH SYMMETRIES

Published online by Cambridge University Press:  09 June 2003

MANUEL DEL PINO
Affiliation:
Departamento de Ingeniería, Matemática and CMM, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile
PATRICIO FELMER
Affiliation:
Departamento de Ingeniería, Matemática and CMM, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile
MONICA MUSSO
Affiliation:
Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi, 24 – 10129 Torino, [email protected]
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Abstract

The aim of this paper is to show the existence of solutions with an arbitrarily large number of bubbles for the slightly super-critical elliptic problem $-\Delta u=u^{{(N+2)/(N-2)} +\ve }$ in $\Omega$, subject to the conditions that $u>0$ in $\Omega$, and $u=0$ on $\partial \Omega$, where $\ve >0$ is a small parameter and $\Omega \subset \RR^N$ is a bounded domain with certain symmetries, for instance an annulus or a torus in $\RR^3$.

Type
Notes and Papers
Copyright
© The London Mathematical Society 2003

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