Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 147, pp. 1-18.
Title: Generalized scalar curvature type equation
on complete Riemannian manifolds
Author: Mohammed Benalili (Univ. Aboubekr Belkaid, Tlemcen, Algerie)
Youssef Maliki (Univ. Aboubekr Belkaid, Tlemcen, Algerie)
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.