Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T18:52:37.685Z Has data issue: false hasContentIssue false
  • English
  • Français

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, [email protected]
K. Sandeep
Affiliation:
TIFR Centre, IISc Campus, PO Box 1234, Bangalore-560 012, [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)