A semilinear elliptic equation with competing powers and a radial potential

2017/12/12 by Musso, M., Pimentel, J.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1712.04293

Abstract

We verify the existence of radial positive solutions for the semi-linear equation - Δu=u^p - V(y) u^q, ugt;0, in ℝ^N where N≥ 3, p is close to p^*:=(N+2)/(N-2), and V is a radial smooth potential. If q is super-critical, namely q>p^*, we prove that this Problem has a radial solution behaving like a super-position of bubbles blowing-up at the origin with different rates of concentration, provided V(0)<0. On the other hand, if N/(N-2)

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