IUMJ

Title: Henon type equations and concentration on spheres

Authors: Filomena Pacella and Ederson Moreira dos Santos

Issue: Volume 65 (2016), Issue 1, 273-306

Abstract:

In this paper, we study the concentration profile of various kinds of symmetric solutions of some semilinear elliptic problems arising in astrophysics and in diffusion phenomena. Using a reduction method, we prove that doubly symmetric positive solutions in a $2m$-dimensional ball must concentrate and blow up on $(m-1)$-spheres as the concentration parameter tends to infinity. We also consider axially symmetric positive solutions in a ball in $\mathbb{R}^N$, $N\geq3$, and show that concentration and blow-up occur on two antipodal points, as the concentration parameter tends to infinity.