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http://dx.doi.org/10.4134/JKMS.j210091

RADIAL SYMMETRY OF POSITIVE SOLUTIONS TO A CLASS OF FRACTIONAL LAPLACIAN WITH A SINGULAR NONLINEARITY  

Cao, Linfen (College of Mathematics and Information Science Henan Normal University)
Wang, Xiaoshan (School of Mathematical Sciences Nanjing Normal University)
Publication Information
Journal of the Korean Mathematical Society / v.58, no.6, 2021 , pp. 1449-1460 More about this Journal
Abstract
In this paper, we consider the following nonlocal fractional Laplacian equation with a singular nonlinearity (-∆)su(x) = λuβ (x) + a0u-γ (x), x ∈ ℝn, where 0 < s < 1, γ > 0, $1<{\beta}{\leq}\frac{n+2s}{n-2s}$, λ > 0 are constants and a0 ≥ 0. We use a direct method of moving planes which introduced by Chen-Li-Li to prove that positive solutions u(x) must be radially symmetric and monotone increasing about some point in ℝn.
Keywords
Fractional Laplacian; negative powers; method of moving planes;
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