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

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.