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- W4286892289 abstract "We study the existence/nonexistence and qualitative properties of the positive solutions to the problem begin{align*} (-Delta)^s u -thetafrac{u}{|x|^{2s}}&=u^p - u^q quadtext{in },, mathbb{R}^N,quad u > 0 quadtext{in },, mathbb{R}^N, quad u in dot{H}^s(mathbb{R}^N)cap L^{q+1}(mathbb{R}^N), end{align*} where $sin (0,1)$, $N>2s$, $q>pgeq{(N+2s)}/{(N-2s)}$, $thetain(0, Lambda_{N,s})$ and $Lambda_{N,s}$ is the sharp constant in the fractional Hardy inequality. For qualitative properties of the solutions we mean, both the radial symmetry that is obtained by using the moving plane method in a nonlocal setting on the whole $mathbb{R}^N$, and upper bound behavior of the solutions. To this last end we use a representation result that allows us to transform the original problem into a new nonlocal problem in a weighted fractional space." @default.
- W4286892289 created "2022-07-25" @default.
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- W4286892289 date "2021-10-27" @default.
- W4286892289 modified "2023-09-27" @default.
- W4286892289 title "Fractional Hardy equations with critical and supercritical exponents" @default.
- W4286892289 doi "https://doi.org/10.48550/arxiv.2110.14414" @default.
- W4286892289 hasPublicationYear "2021" @default.
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