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 $Ksubset M$ and some $alpha in (0,1)$.