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Finite Morse Index Solutions of the Fractional Henon-Lane-Emden Equation with Hardy Potential

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Title
Finite Morse Index Solutions of the Fractional Henon-Lane-Emden Equation with Hardy Potential
Author
Kim, SoojungLee, Youngae
Issue Date
2021-12
Publisher
MATHEMATICAL SOC REP CHINA
Citation
TAIWANESE JOURNAL OF MATHEMATICS
Abstract
In this paper, we study the fractional Henon-Lane-Emden equation associated with Hardy potential (-Delta)(s)u-gamma vertical bar x vertical bar(-2s) u=vertical bar x vertical bar(a)vertical bar u vertical bar(p-1)u in R-n. Extending the celebrated result of [14], we obtain a classification result on finite Morse index solutions to the fractional elliptic equation above with Hardy potential. In particular, a critical exponent p of Joseph-Lundgren type is derived in the supercritical case studying a Liouville type result for the s-harmonic extension problem.
URI
https://scholarworks.unist.ac.kr/handle/201301/56569
URL
https://projecteuclid.org/journals/taiwanese-journal-of-mathematics/volume--1/issue--1/Finite-Morse-Index-Solutions-of-the-Fractional-HenonLaneEmden-Equation-with/10.11650/tjm/211203.full
DOI
10.11650/tjm/211203
ISSN
1027-5487
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