Uniqueness of positive solutions to fractional nonlinear elliptic equations with harmonic potential

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CRMATH_2025__363_G4_353_0.pdf(399.04 KB)
Date
2025-06-02
Authors
Tianxiang, Gou
Radulescu, Vicentiu
ORCID
0000-0003-4615-5537
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Referee
Mark
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The French Academy of sciences
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Abstract
In this paper, we establish the uniqueness of positive solutions to the following fractional nonlinear elliptic equation with harmonic potential: (MATHEMATICAL FOMULA PRESENTED) where (MATHEMATICAL EQUATION PRESENTED) is the lowest eigenvalue of the operator ()s + |x|2. This solves an open question raised in [15] concerning the uniqueness of solutions to the equation.
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Keywords
fractional elliptic equations, harmonic potential, positive solutions, Uniqueness
Citation
COMPTES RENDUS MATHEMATIQUE. 2025, vol. 363, issue 1, p. 353-363.
https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.716/
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Peer-reviewed
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en
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Creative Commons Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
DOI
10.5802/crmath.716
URI
https://hdl.handle.net/11012/251326
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