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• W3184450021 abstract "In this paper we study the existence, multiplicity and regularity of positive weak solutions for the following Kirchhoff-Choquard problem: begin{equation*} begin{array}{cc} displaystyle Mleft( iintlimits_{mathbb{R}^{2N}} frac{|u(x)-u(y)|^2}{|x-y|^{N+2s}},dxdyright) (-Delta)^s u = frac{lambda}{u^gamma} + left( intlimits_{Omega} frac{|u(y)|^{2^{*}_{mu ,s}}}{|x-y|^ mu}, dyright) |u|^{2^{*}_{mu ,s}-2}u ;text{in} ; Omega, %quad quad u > 0quad text{in} ; Omega, quad quad u = 0quad text{in} ; mathbb{R}^{N}backslashOmega, end{array} end{equation*} where $Omega$ is open bounded domain of $mathbb{R}^{N}$ with $C^2$ boundary, $N > 2s$ and $s in (0,1)$. $M$ models Kirchhoff-type coefficient in particular, the degenerate case where Kirchhoff coefficient M is zero at zero. $(-Delta)^s$ is fractional Laplace operator, $lambda > 0$ is a real parameter, $gamma in (0,1)$ and $2^{*}_{mu ,s} = frac{2N-mu}{N-2s}$ is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality. We prove that each positive weak solution is bounded and satisfy Holder regularity of order $s$. Furthermore, using the variational methods and truncation arguments we prove the existence of two positive solutions." @default.
• W3184450021 created "2021-08-02" @default.
• W3184450021 creator A5072035531 @default.
• W3184450021 creator A5091590136 @default.
• W3184450021 date "2021-07-14" @default.
• W3184450021 modified "2023-10-16" @default.
• W3184450021 title "Multiple positive solutions for degenerate Kirchhoff equations with singular and Choquard nonlinearity" @default.
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• W3184450021 doi "https://doi.org/10.1002/mma.7659" @default.
• W3184450021 hasPublicationYear "2021" @default.
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