Generalized scalar curvature type equation on complete Riemannian manifolds

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 C1,ɑ(K) for any compact set K ⊂ M and some α ∈ (0, 1).