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Applicable Analysis
An International Journal
Volume 97, 2018 - Issue 4
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Articles

On the eigenvalues and Fučik spectrum of p-fractional Hardy-Sobolev operator with weight function

Pages 633-658 | Received 17 Aug 2016, Accepted 09 Jan 2017, Published online: 23 Jan 2017
 

Abstract

In this article, we study the nonlinear eigenvalue problem of fractional Hardy–Sobolev operator

where is a bounded domain in with Lipschitz boundary containing 0, , , , and the weight function V, having nontrivial positive part, belongs to suitable integrable class and may change sign. We investigate some properties of the first eigenvalue such as simplicity and isolation. Moreover, we also study the Fučik spectrum of fractional Hardy-Sobolev operator, which is defined as the set such that

has a non-trivial solution u. We show the existence of a first nontrivial curve of this spectrum and also we prove some properties of this curve. At the end, we study a nonresonance problem with respect to the weighted Fučik spectrum.

AMS Subject Classifications:

Notes

No potential conflict of interest was reported by the author.

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