Positive solutions for indefinite inhomogeneous Neumann elliptic problems

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.

Keywords

• p-Laplacian
• nonlinear boundary conditions
• indefinite and critical nonlinearities.