  In this study, we consider a boundary value problem generated by the
Sturm-Liouville problem with a frozen argument and with non-separated boundary
conditions on a time scale. Firstly, we present some solutions and
characteristic function of the problem on an arbitrary bounded time scale.
Secondly, we prove some properties of eigenvalues and obtain a formulation for
the eigenvalues-number on a finite time scale. Finally, we give an asymptotic
formula for eigenvalues of the problem on another special time scale.
