  In this paper, we obtain lower bounds for the first eigenvalue to some kinds
of the eigenvalue problems for Bi-drifted Laplacian operator on compact
manifolds (also called a smooth metric measure space) with boundary and
$m$-Bakry-Emery Ricci curvature or Bakry-Emery Ricci curvature bounded below.
We also address the eigenvalue problem with Wentzell-type boundary condition
for drifted Laplacian on smooth metric measure space.
