In this study, we are concerned with spectral problems of second-order vectordynamic equations with two-point boundary value conditions and mixedderivatives, where the matrix-valued coefficient of the leading term may besingular, and the domain is non-uniform but finite. A concept ofself-adjointness of the boundary conditions is introduced. The self-adjointnessof the corresponding dynamic operator is discussed on a suitable admissiblefunction space, and fundamental spectral results are obtained. The dualorthogonality of eigenfunctions is shown in a special case. Extensions toeven-order Sturm-Liouville dynamic equations, linear Hamiltonian and symplecticnabla systems on general time scales are also discussed.
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