Overview of Weyl-Titchmarsh theory for second order Sturm-Liouville equations on time scales

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Authors	ŠIMON HILSCHER Roman ZEMÁNEK Petr
Year of publication	2011
Type	Article in Periodical
Magazine / Source	Int. J. Difference Equ.
MU Faculty or unit	Faculty of Science
Citation
Field	General mathematics
Keywords	Time scale; Weyl-Titchmarsh theory; Second order Sturm-Liouville dynamic equation; m(λ)-function; Weyl disk; Weyl circle; Limit point case; Limit circle case
Attached files	ijde_secorderwt.pdf
Description	In this paper we present an overview of the basic Weyl-Titchmarsh theory for second order Sturm-Liouville equations on time scales. We construct m(lambda)-function, the Weyl solution, and Weyl disk. We justify the terminology ``disk'' by its geometric properties, show explicitly the coordinates of the center of the disk, and calculate its radius. We show that the dichotomy regarding the square-integrable solutions known in the continuous time and discrete theory works in the same way for general time scales.
Related projects:	Mathematical structures and their physical applications Oscillation and spectral theory of differential and difference systems Matematické struktury