Sturm-Liouville eigenvalue problems on time scales. (English) Zbl 0938.34015

Summary: For Sturm-Liouville eigenvalue problems on time scales with separated boundary conditions the authors give an oscillation theorem and establish Rayleigh’s principle. The results not only unify the corresponding theories for differential and difference equations, but are also new in the discrete case.


34B24 Sturm-Liouville theory
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
39A10 Additive difference equations
93C70 Time-scale analysis and singular perturbations in control/observation systems
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