Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 155, pp. 1-9.

Title: Solving p-Laplacian equations on complete manifolds

Authors: Mohammed Benalili (Univ. Abou-Bekr Belkaid, Algerie)
         Youssef Maliki    (Univ. Abou-Bekr Belkaid, Algerie)
	 
Abstract: 
 Using a reduced version of the sub and super-solutions method, 
 we prove that the equation 
 $\Delta _{p}u+ku^{p-1}-Ku^{p^{\ast }-1}=0$
 has a positive solution on a complete Riemannian manifold for 
 appropriate functions $k,K:M\to \mathbb{R}$.
 
Submitted June 28, 2005. Published December 14, 2006.
Math Subject Classifications: 31C45, 53C21.
Key Words: Differential geometry; nonlinear partial 
           differential equations.