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- W4299968340 abstract "In this paper we consider the following critical nonlocal problem $$ left{begin{array}{ll} Mleft(displaystyleiint_{mathbb{R}^{2N}}frac{|u(x)-u(y)|^2}{|x-y|^{N+2s}}dxdyright)(-Delta)^s u = displaystylefrac{lambda}{u^gamma}+u^{2^*_s-1}&quadmbox{in } Omega, u>0&quadmbox{in } Omega, u=0&quadmbox{in } mathbb{R}^NsetminusOmega, end{array}right. $$ where $Omega$ is an open bounded subset of $mathbb R^N$ with continuous boundary, dimension $N>2s$ with parameter $sin (0,1)$, $2^*_s=2N/(N-2s)$ is the fractional critical Sobolev exponent, $lambda>0$ is a real parameter, exponent $gammain(0,1)$, $M$ models a Kirchhoff type coefficient, while $(-Delta)^s$ is the fractional Laplace operator. In particular, we cover the delicate degenerate case, that is when the Kirchhoff function $M$ is zero at zero. By combining variational methods with an appropriate truncation argument, we provide the existence of two solutions." @default.
- W4299968340 created "2022-10-03" @default.
- W4299968340 creator A5008386861 @default.
- W4299968340 date "2017-03-22" @default.
- W4299968340 modified "2023-09-26" @default.
- W4299968340 title "A fractional Kirchhoff problem involving a singular term and a critical nonlinearity" @default.
- W4299968340 doi "https://doi.org/10.48550/arxiv.1703.07861" @default.
- W4299968340 hasPublicationYear "2017" @default.
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