Prescribing the Q-curvature on the sphere with conical singularities

Ali  Maalaoui

doi:10.3934/dcds.2016074

Article Contents

2016, Volume 36, Issue 11: 6307-6330. Doi: 10.3934/dcds.2016074

This issue Previous Article Exponential stabilization of a structure with interfacial slip Next Article Groups of asymptotic diffeomorphisms

Prescribing the Q-curvature on the sphere with conical singularities

Ali Maalaoui^1,

1.
Department of mathematics and natural sciences, American University of Ras Al Khaimah, PO Box 10021, Ras Al Khaimah

Received: November 30, 2015

Revised: June 30, 2016

Published: May 2017

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Abstract

In this paper we investigate the problem of prescribing the $Q$-curvature, on the sphere of any dimension with prescribed conical singularities. We also give the asymptotic behaviour of the solutions that we find and we prove their uniqueness in the negative curvature case. We focus mainly on the odd dimensional case, more specifically the three dimensional sphere.

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Mathematics Subject Classification: Primary: 53C21; Secondary: 35Q82.

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