# American Institute of Mathematical Sciences

July  2005, 12(4): 747-760. doi: 10.3934/dcds.2005.12.747

## Super-position of spikes for a slightly super-critical elliptic equation in $R^N$

 1 Dipartimento di Matematica Applicata "U.Dini", Università di Pisa, Via Bonanno 25B - 56126 Pisa, Italy 2 Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy 3 Dipartimento di Metodi e Modelli Matematici, Università di Roma "La Sapienza", Via Scarpa, 16 - 00166 Roma, Italy

Received  October 2003 Revised  November 2004 Published  January 2005

We prove existence of radial positive solutions for the equation

$-\Delta u + V(y) u =u^{\frac{N+2}{N-2}+\varepsilon} \quad$ in $\quad \mathbb R^N$

where the potential $V$ is a radial smooth function with $V(0)<0$.
In particular, we show that the solutions have the shape of a super-position of spikes blowing-up at the origin as $\varepsilon \to 0$, with different rates of concentration.

Citation: A. M. Micheletti, Monica Musso, A. Pistoia. Super-position of spikes for a slightly super-critical elliptic equation in $R^N$. Discrete and Continuous Dynamical Systems, 2005, 12 (4) : 747-760. doi: 10.3934/dcds.2005.12.747
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