Multiplicity of positive solutions for the generalized Hénon equation with fractional Laplacian

A. P. Shcheglova

Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 48, Tome 489 (2020), pp. 207-224

Résumé

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 $2<q<\dfrac{2n}{n-2s}$ and sufficiently large $\alpha$. Also the existence of a radial solution for some supercritical values of the $q$ and sufficiently large $\alpha$ is proved.

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