Table of Contents
Geometry
Volume 2014, Article ID 582367, 9 pages
http://dx.doi.org/10.1155/2014/582367
Research Article

Existence and Multiplicity Results for the Scalar Curvature Problem on the Half-Sphere

Department of Mathematics and Computer Science, University of Monastir, I.P.E.I.M., Avenue Ibn Al Jazzar, 5019 Monastir, Tunisia

Received 3 June 2013; Accepted 27 January 2014; Published 20 March 2014

Academic Editor: Constantin Udriste

Copyright © 2014 Ridha Yacoub. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper we deal with the scalar curvature problem under minimal boundary mean curvature condition on the standard 3-dimensional half-sphere. Using tools related to the theory of critical points at infinity, we give existence results under perturbative and nonperturbative hypothesis, and with the help of some “Morse inequalities at infinity”, we provide multiplicity results for our problem.