Hénon type equations and concentration on spheres

2014/07/24 by Santos, Ederson Moreira dos, Pacella, Filomena
#35B06 #35B07 #35B40 #35J15 #35J61 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1407.6581

Abstract

In this paper we study the concentration profile of various kind 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 ℝ^N, N ≥ 3, and show that concentration and blow up occur on two antipodal points, as the concentration parameter tends to infinity.

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