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 $\Omega\subseteq \mathbb{R}^N$ is an open bounded domain with smooth boundary containing 0 in its interior, $N>2s$ with $s\in(0,1)$, $0<q<1$, $0<\mu<N$, $\gamma$ and $\lambda$ are positive parameters, $\theta\in [1, p)$ with $1 < p < 2^*_{\mu,s,\alpha}$, where $2^*_{\mu,s,\alpha}$ is the upper critical exponent in the sense of weighted Hardy-Littlewood-Sobolev inequality. Moreover $M$ 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
Tarun Sharma
Department of Mathematics
Bennett University
Greater Noida, Uttar Pradesh, India
email: tarunsharma80065@gmail.com

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