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Existence and non-existence of the first eigenvalue of the perturbed Hardy–Sobolev operator

  • Adimurthi (a1) and K. Sandeep (a2)

Abstract

In this paper we study the existence, non-existence and simplicity of the first eigenvalue of the perturbed Hardy-Sobolev operator under various assumptions on the perturbation q. We study the asymptotic behaviour of the first eigenfunction near the origin when the perturbation q is q = s, 0 < s < 1. We will also establish the best constant in a Hardy-Sobolev inequality proved by Adimurthi et al.

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