Bubble tower solutions for a supercritical elliptic problem in R-N

Abstract

We consider the problem {-Delta u + u = u(p) + lambda u(q) u > 0 in R-Nu(z) -> 0 as vertical bar z vertical bar -> infinity where p = p* + epsilon, with p* = N+2/N-2, while 1 < q < N+2/N-2 if N >= 4, and 3 < q < 5 if N = 3, lambda > 0, and epsilon is a positive parameter. We prove that for epsilon > 0 small enough, the problem has a solution with the shape of a tower of bubbles.