Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 106, pp. 1-10.

Title: A reduction method for proving the existence of solutions 
       to elliptic equations involving the p-laplacian 

Authors: Mohamed Benalili (Univ. Abou-Bakr BelKaid, Algerie)
 Youssef Maliki (Univ. Abou-Bakr BelKaid, Algerie)

Abstract: 
   We introduce a reduction method for proving the existence of
  solutions to elliptic equations involving the p-Laplacian operator.
  The existence of solutions is implied by the existence of a positive
  essentially weak subsolution on a manifold and the existence of a
  positive supersolution on each compact domain of this manifold.
  The existence and nonexistence of positive supersolutions is given
  by the sign of the first eigenvalue of a nonlinear operator.
 
Submitted March 10, 2003. Published October 21, 2003.
Math Subject Classifications: 58J05, 53C21.
Key Words: Analysis on manifolds; semi-linear elliptic PDE.