Electron. J. Differential Equations, Vol. 2022 (2022), No. 25, pp. 1-29.
Fractional Kirchhoff Hardy problems with weighted Choquard and singular nonlinearity
Sarika Goyal, Tarun Sharma
Abstract:
In this article, we study the existence and multiplicity of solutions to the
fractional Kirchhoff Hardy problem involving weighted Choquard and singular nonlinearity

where
is an open bounded domain with smooth boundary
containing 0 in its interior,
with
,
,
,
and
are positive parameters,
with
, where
is the upper critical exponent
in the sense of weighted Hardy-Littlewood-Sobolev inequality.
Moreover
models a Kirchhoff coefficient, l is a positive weight and r is a
sign-changing function. Under the suitable assumption on l and r, we established
the existence of two positive solutions to the above problem by Nehari-manifold and
fibering map analysis with respect to the parameters.The results obtained
here are new even for s=1.
Submitted December 30, 2021. Published March 25, 2022.
Math Subject Classifications: 35A15, 35J75, 36B38.
Key Words: Fractional Kirchhoff Hardy operator; singular nonlinearity;
\hfill\break\indent weighted Choquard type nonlinearity;
Nehari-manifold; fibering map.
DOI: https://doi.org/10.58997/ejde.2022.25
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Sarika Goyal
Department of Mathematics
Bennett University
Greater Noida, Uttar Pradesh, India
email: sarika1.iitd@gmail.com
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Tarun Sharma
Department of Mathematics
Bennett University
Greater Noida, Uttar Pradesh, India
email: tarunsharma80065@gmail.com
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