Geodesic
Multiplicity of positive solutions for the generalized H\'enon equation with fractional Laplacian
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 48, Tome 489 (2020), pp. 207-224

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We consider the equation $(-\Delta)^s u=|x|^{\alpha}|u|^{q-2}u$ in the unit ball. We show that there exist arbitratily many nonequivalent positive solutions for $2$ and sufficiently large $\alpha$. Also the existence of a radial solution for some supercritical values of the $q$ and sufficiently large $\alpha$ is proved. 
@article{ZNSL_2020_489_a9,
     author = {A. P. Shcheglova},
     title = {Multiplicity of positive solutions for the generalized {H\'enon} equation with fractional {Laplacian}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {207--224},
     publisher = {mathdoc},
     volume = {489},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_489_a9/}
}
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A. P. Shcheglova. Multiplicity of positive solutions for the generalized H\'enon equation with fractional Laplacian. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 48, Tome 489 (2020), pp. 207-224. http://geodesic.mathdoc.fr/item/ZNSL_2020_489_a9/