Year: 2020
Author: Weiwei Ao, Hardy Chan, Azahara DelaTorre, Marco A. Fontelos, María del Mar González, Juncheng Wei
Journal of Mathematical Study, Vol. 53 (2020), Iss. 4 : pp. 370–401
Abstract
Non-local equations cannot be treated using classical ODE theorems. Nevertheless, several new methods have been introduced in the non-local gluing scheme of our previous article; we survey and improve those, and present new applications as well. First, from the explicit symbol of the conformal fractional Laplacian, a variation of constants formula is obtained for fractional Hardy operators. We thus develop, in addition to a suitable extension in the spirit of Caffarelli–Silvestre, an equivalent formulation as an infinite system of second order constant coefficient ODEs. Classical ODE quantities like the Hamiltonian and Wrońskian may then be utilized. As applications, we obtain a Frobenius theorem and establish new Pohožaev identities. We also give a detailed proof for the non-degeneracy of the fast-decay singular solution of the fractional Lane–Emden equation.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v53n4.20.01
Journal of Mathematical Study, Vol. 53 (2020), Iss. 4 : pp. 370–401
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: ODE methods non-local equations fractional Hardy operators Frobenius theorem.