Multiple Solutions for a Henon-Like Equation on the Annulus

2007/05/10 by Calanchi, Marta, Secchi, Simone, Terraneo, Elide
#35J40 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0705.1492

Abstract

For the equation (-Δu = | |x|-2 |^αu^p-1), (1 < |x| < 3), we prove the existence of two solutions for (α) large, and of two additional solutions when (p) is close to the critical Sobolev exponent (2^*=2N/(N-2)). A symmetry--breaking phenomenon appears, showing that the least--energy solutions cannot be radial functions.

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