On positive solutions of indefinite inhomogeneous Neumann boundary value problems

Abstract

In this paper, we study a class of inhomogeneous Neumann boundary value problems on a compact Riemannian manifold with boundary where indefinite and critical nonlinearities are included. Applying the fibering approach 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.