  In this paper, we study the spectral problem on a compact Finsler manifold
with or without boundary. More precisely, given a certain collection of sets in
Sobolev space $H^{1,2}(M)$ and a dimension-like function, we can define a
corresponding spectrum. Such a spectrum satisfies nice properties. In
particular, the eigenfunction corresponding to each eigenvalue always exists.
And a Cheng type upper bound estimate for eigenvalues is obtained. Moreover,
some interesting examples are constructed and investigated in this paper.
