Weak KAM theorem for Hamilton‐Jacobi equations with Neumann boundary conditions on noncompact manifolds

Abstract

In this paper, we consider Hamilton-Jacobi equations with homogeneous Neumann boundary condition. We establish some results on noncompact manifold with homogeneous Neumann boundary conditions in view of weak KolmogorovArnold-Moser (KAM) theory, which is a generalization of the results obtained by Fathi under the non-bounded condition.