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

Abstract

We prove existence of radial positive solutions for the equation

-Delta u + V(y)u + u((N+2/N-2)+ epsilon) in 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 is an element of -> 0, with different rates of concentration.