Eigenvalues of second-order symmetric equations on time scales with periodic and antiperiodic boundary conditions

This paper studies periodic and antiperiodic boundary value problems for second-order symmetric linear equations on time scales. By properties of eigenvalues of the Dirichlet boundary value problem and some oscillation results, existence of eigenvalues of these two different boundary value problems is proved, numbers of their eigenvalues are calculated, and their relationships are obtained. These results not only unify the existing ones of periodic and antiperiodic boundary value problems for second-order symmetric differential and difference equations but also contain more complicated time scales.