Electron. J. Diff. Eqns., Vol. 2004(2004), No. 147, pp. 1-18.

Generalized scalar curvature type equation on complete Riemannian manifolds

Mohammed Benalili, Youssef Maliki

Abstract:
In this work, we investigate positive solutions for a quasilinear elliptic equation on complete manifold $M$. This equation extends to the $p$-Laplacian the equation of the prescribed scalar curvature. A minimizing sequence is constructed which converges to a non trivial solution belonging to $C^{1,\alpha }(K)$ for any compact set $K\subset M$ and some $\alpha \in (0,1)$.

Submitted November 26, 2004. Published December 13, 2004.
Math Subject Classifications: 58J05.
Key Words: Complete manifolds; p-Laplacian; critical Sobolev exponent.

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Mohamed Benalili
Faculté des Sciences, Dept. de Mathématiques
B. P. 119, Université Aboubekr Belkaïd, Tlemcen, Algerie
email: m_benalili@mail.univ-tlemcen.dz
Youssef Maliki
Faculté des Sciences, Dept. de Mathématiques
B. P. 119, Université Aboubekr Belkaïd, Tlemcen, Algerie
email: m-youssef@mail.univ-tlemcen.dz

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