"Bubble-Tower" phenomena in a semilinear elliptic equation with mixed Sobolev growth

Abstract

In this work we consider the following problem [GRAPHICS]

with N/(N - 2) < p < p* = (N + 2)/(N - 2) < q, N >= 3.

We prove that if p is fixed, and q is close enough to the critical exponent p*, then there exists a radial solution which behaves like a superposition of bubbles of different blow-up orders centered at the origin. Similarly when q is fixed and p is sufficiently close to the critical, we prove the existence of a radial solution which resembles a superposition of flat bubbles centered at the origin.