Eigenvalues of second-order linear equations with coupled boundary conditions on time scales (Q980410)

The authors consider a coupled boundary eigenvalue problem of the form \[ -(p(t)y^\Delta(t))^\Delta + q(t) y^\sigma(t) = \lambda r(t) y^\sigma(t) \] with \[ \binom {y(1)}{y^\Delta(1)}= e^{i\alpha} K\binom {y(\rho(0))}{y^\Delta(\rho(0))} \] on a general time scale. The main objective is to guarantee existence of eigenvalues and compute their multiplicities under certain conditions on the matrix \(K\) and exponent \(\alpha\). The results are extensions of known ones from difference equations to the general time scales setting.