Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 57, pp. 1-21.

Title: Positive solutions for indefinite inhomogeneous Neumann
       elliptic problems

Authors: Yavdat Il'yasov (Univ. de La Rochelle, France)
         Thomas Runst (Friedrich-Schiller-Univ., Jena, Germany)

Abstract: 
  We consider a class of inhomogeneous Neumann boundary-value
  problems on a compact Riemannian manifold with boundary
  where indefinite and  critical nonlinearities are
  included. We introduce a new and, in some sense, more
  general variational approach to these problems. Using this
  idea we prove new results on the existence and
  multiplicity of positive solutions.
 
Submitted January 10, 2003. Published May 19, 2003.
Math Subject Classifications: 35J70, 35J65, 47H17.
Key Words: p-Laplacian; nonlinear boundary conditions;
           indefinite  and critical nonlinearities.