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

Published online by Cambridge University Press:  12 July 2007

Adimurthi  and
K. Sandeep
Adimurthi
Affiliation:
TIFR Centre, IISc Campus, PO Box 1234, Bangalore-560 012, Indiaaditi@math.tifrbng.res.in
K. Sandeep
Affiliation:
TIFR Centre, IISc Campus, PO Box 1234, Bangalore-560 012, Indiasandeep@math.tifrbng.res.in
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Abstract

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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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 5 , October 2002 , pp. 1021 - 1043
Copyright
Copyright © Royal Society of Edinburgh 2002