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.
Notes
No potential conflict of interest was reported by the author.