Nondegeneracy of positive solutions to nonlinear Hardy-Sobolev equations

2016/12/09 by Robert, Frédéric · 2 citations
#35J20 #35J60 #35J75 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1612.02935

Abstract

In this note, we prove that the kernel of the linearized equation around a positive energy solution in ℝⁿ, n≥ 3, to -ΔW-γ|x|^-2V=|x|^-sW^{2^⋆(s)-1} is one-dimensional when s+γ>0. Here, s∈ [0,2), 0≤γ

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• Existence of Bianchi-Egnell stability extremizer for the Hardy-Sobolev inequality
• Ground-state blowing-up solutions for a Hardy-Sobolev equations on a manifold

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