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.

Full text not available from this repository.

Official URL: http://edoc.unibas.ch/42416/

Downloads: Statistics Overview

## Abstract

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.

(-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 |

ISSN: | 1120-6330 |

Note: | Publication type according to Uni Basel Research Database: Journal article |

Related URLs: | |

Last Modified: | 22 Nov 2016 09:29 |

Deposited On: | 22 Nov 2016 09:29 |

Repository Staff Only: item control page