Multiplicity of Positive Solutions for the Generalized HÉnon Equation with Fractional Laplacian

It is proved that the equation (−Δ) s u = |x| α |u| q−2 u has arbitrarily many nonequivalent positive solutions in the unit ball for 2 < q < 2 n n − 2 s and sufficiently large α. Also the existence of radial solution for some supercritical values of q and sufficiently large α is proved....

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2022, Vol.260 (1), p.142-154
Main Author: Shcheglova, A. P.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:It is proved that the equation (−Δ) s u = |x| α |u| q−2 u has arbitrarily many nonequivalent positive solutions in the unit ball for 2 < q < 2 n n − 2 s and sufficiently large α. Also the existence of radial solution for some supercritical values of q and sufficiently large α is proved.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-021-05678-8