Existence of entire solutions to a fractional Liouville equation in R-n

Hyder, Ali. (2016) Existence of entire solutions to a fractional Liouville equation in R-n. Rendiconti Lincei. Matematica e applicazioni, 27 (1). pp. 1-14.

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We study the existence of solutions to the problem
(-Delta)(n/2)u=Qe(nu) in R-n; V:= integral(Rn) e(nu) dx < infinity,
where Q - (n - 1)! or Q = -(n - 1)!. Extending the works of Wei-Ye and Hyder-Martinazzi to arbitrary odd dimension n >= 3 we show that to a certain extent the asymptotic behavior of u and the constant V can be prescribed simultaneously. Furthermore if Q = -(n - 1)! then V can be chosen to be any positive number. This is in contrast to the case n = 3, Q - 2, where Jin-Maalaoui-Martinazzi-Xiong showed that necessarily V <=vertical bar S-3 vertical bar, and to the case n = 4, Q = 6, where C-S. Lin showed that V <=vertical bar S-4 vertical bar.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik
UniBasel Contributors:Hyder, Ali
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Accademia nazionale dei Lincei
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:22 Nov 2016 09:29
Deposited On:22 Nov 2016 09:29

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