Multiplicity results for the prescribed scalar curvature on low spheres
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 7 (2008) no. 4, p. 609-634

In this paper, we consider the problem of multiplicity of conformal metrics of prescribed scalar curvature on standard spheres đť•Š 3 ,đť•Š 4 . Under generic conditions we establish some Morse Inequalities at Infinity, which give a lower bound on the number of solutions to the above problem in terms of the total contribution of its critical points at Infinity to the difference of topology between the level sets of the associated Euler-Lagrange functional. As a by-product of our arguments we derive a new existence result on đť•Š 4 through an Euler-Hopf type formula.

Classification:  58E05,  35J65,  53C21,  35B40
@article{ASNSP_2008_5_7_4_609_0,
     author = {Ben Ayed, Mohamed and Ould Ahmedou, Mohameden},
     title = {Multiplicity results for the prescribed scalar curvature on low spheres},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 7},
     number = {4},
     year = {2008},
     pages = {609-634},
     zbl = {1213.58009},
     mrnumber = {2483638},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2008_5_7_4_609_0}
}
Ben Ayed, Mohamed; Ould Ahmedou, Mohameden. Multiplicity results for the prescribed scalar curvature on low spheres. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 7 (2008) no. 4, pp. 609-634. http://www.numdam.org/item/ASNSP_2008_5_7_4_609_0/

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