Sturm-Picone comparison theorem for matrix systems on time scales

A Nonlinear Sturm–Picone Comparison Theorem for Dynamic Equations on Time Scales

The authors derive an analog of the well-known Picone identity but for nonlinear dynamic equations on time scales. As a consequence, they obtain a nonlinear comparison theorem in the spirit of the classical Sturm–Picone comparison theorem. Comparison results yielding the nonoscillation of all solutions of nonlinear equations are also obtained. AMS subject classification: 34C10, 34C15, 39A11.

Sturm-Picone Comparison Theorem of Second-Order Linear Equations on Time Scales

Sturm–liouville Operators on Time Scales

We establish the connection between Sturm–Liouville equations on time scales and Sturm–Liouville equations with measure-valued coefficients. Based on this connection we generalize several results for Sturm–Liouville equations on time scales which have been obtained by various authors in the past.

An Expansion Theorem for a Sturm–Liouville Operator on Semi-Unbounded Time Scales

In this study, we establish a Parseval equality and an expansion formula for a Sturm– Liouville operator on semi-unbounded time scales. AMS subject classification: 34L10.

Eigenfunction Expansions for a Sturm–Liouville Problem on Time Scales

In this paper we investigate a Sturm–Liouville eigenvalue problem on time scales. Existence of the eigenvalues and eigenfunctions is proved. Mean square convergent and uniformly convergent expansions in the eigenfunctions are established. AMS subject classification: 34L10.