Combined Effects of Singular and Hardy Nonlinearities in Fractional Kirchhoff Choquard Equation
Year: 2025
Type: article
Abstract: The aim of this paper is to investigate the existence and the multiplicity of solutions to the singular Kirchhoff non-local problem with Hardy and Choquard nonlinearities. The problem is defined as follows: $ \begin{equation*} \left\{ \begin{array}{ll} &\quad M\Big( \int_{\mathbb{R}^{2N}}\frac{|u(x)-u(y)|^{p}}{|x-y|^{N+sp}}dx dy\Big) -\Delta^s_p u-\alpha \frac{|u|^{p-2}u}{|x|^{sp}}\\ &=\lambda f(x) u^{-\gamma}+ g(x) \Big( \int_{\Omega}\frac{u^{p_{\mu, s}^*}(y)}{|x-y|^\mu}dy\Big)u^{p_{\mu, s}^*-1} \; \text{in}\; \Omega, \\ &u>0, \;\;\;\;\quad \text{in }\Omega, \\ &u=0, \;\;\;\;\quad \text{in }\mathbb{R}^{N}\setminus \Omega, \end{array} \right. \end{equation*} $ where, $ \Omega\subset \mathbb{R}^N $ is a bounded domain, $ s\in (0, 1) $, $ N>sp $, $ \gamma\in (0, 1), $ $ \alpha, $ $ \lambda $ are two positive real parameters $ 0<\mu 0, b>0 $ and $ \theta\in \Big(1, \min\{ 2p_{\mu, s}^*/p, p_{\mu, s}^*\}\Big). $ Furthermore, $ f $ is a non-negative weight and $ g $ is a sign-changing weight. The novelty in this work lies in the combination of a fractional framework and a singular term with the Hardy and Choquard nonlinearities. To establish the existence of at least two positive solutions for the problem, the Nehari manifold approach is employed.
DOI: 10.11948/20230429
Authors: Rana Alkhal, Mouna Kratou, Kamel Saoudi
Institution: Imam Abdulrahman Bin Faisal University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4411533607