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

Eigenvalues of the Sturm-Liouville problem with a frozen argument on time scales