In this study, we explore an eigenvalue problem on a bounded time scales interval for self-adjoint second order dynamic equations with self-adjoint separated boundary conditions. Existence of the eigenvalues and eigenfunctions is shown. Next, mean square convergent and uniformly convergent expansions in eigenfunctions are established.
In this study, we investigate the eigenvalues and eigenvectors of a quadratic pencil of q-difference equations. The results obtained are then used to solve the corresponding system of differential equations with boundary and initial conditions and zero conditions at infinity.