Picone type identities and definiteness of quadratic functionals on time scales

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Authors	ŠIMON HILSCHER Roman ZEIDAN Vera Michel
Year of publication	2009
Type	Article in Periodical
Magazine / Source	Applied Mathematics and Computation
MU Faculty or unit	Faculty of Science
Citation
Field	General mathematics
Keywords	Time scale; Time scale symplectic system; Linear Hamiltonian system; Discrete symplectic system; Picone identity; Quadratic functional; Nonnegativity; Positivity; Conjoined basis; Controllability; Normality
Description	In this paper we derive a new sufficient condition for the nonnegativity of time scale quadratic functionals associated to time scale symplectic systems. To establish this result, a new global Picone formula is derived. Another proof of a special case of the result is shown to be obtained via a Sturmian comparison technique. Furthermore, we derive several new Picone type identities which, in particular, do not impose a certain delta-differentiability assumption, and we survey known ones from the literature. The results in this paper complete our earlier work on the definiteness of a time scale quadratic functional in terms of its corresponding time scale symplectic system.
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