Growth of the Eigensolutions of Laplacians on Riemannian Manifolds II: Positivity of the Initial Energy

In this paper, the energy function is used to investigate the eigen-solutions of −Δu + 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.