Growth of the eigensolutions of Laplacians on Riemannian manifolds II: positivity of the initial energy

Abstract

In this paper, energy function is used to investigate the eigen-solutions of $-\Delta u+Vu=\lambda u$ on the Riemannian manifolds. We give a new way to prove the positivity of the initial energy of energy function, which leads to a simple way to obtain the growth of eigen-solutions.

Cited by in corpus (2)

• Noncompact complete Riemannian manifolds with dense eigenvalues embedded in the essential spectrum of the Laplacian
• Noncompact complete Riemannian manifolds with singular continuous spectrum embedded into the essential spectrum of the Laplacian, I. The hyperbolic case