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A note on the equivalence between even order Sturm-Liouville equations and symplectic systems on time scales

Basic information
Original title:A note on the equivalence between even order Sturm-Liouville equations and symplectic systems on time scales
Author:Petr Zemánek
Further information
Citation:ZEMÁNEK, Petr. A note on the equivalence between even order Sturm-Liouville equations and symplectic systems on time scales. Applied Mathematics Letters, USA: Elsevier, 2013, vol. 26, No 1, p. 134-139. ISSN 0893-9659. doi:10.1016/j.aml.2012.04.009.Export BibTeX
@article{979812,
author = {Zemánek, Petr},
article_location = {USA},
article_number = {1},
doi = {http://dx.doi.org/10.1016/j.aml.2012.04.009},
keywords = {Time scale; even order Sturm-Liouville dynamic equation; time reversed symplectic system; quadratic functional},
language = {eng},
issn = {0893-9659},
journal = {Applied Mathematics Letters},
title = {A note on the equivalence between even order Sturm-Liouville equations and symplectic systems on time scales},
volume = {26},
year = {2013}
}
Original language:English
Field:General mathematics
Type:Article in Periodical
Keywords:Time scale; even order Sturm-Liouville dynamic equation; time reversed symplectic system; quadratic functional

The 2n-th order Sturm-Liouville differential and difference equations can be written as the linear Hamiltonian differential systems and symplectic difference systems, respectively. In this paper, a similar result is given for the 2n-th order Sturm-Liouville equation on time scales with using time reversed symplectic dynamic systems. Moreover, we show that this transformation preserves the value of the corresponding quadratic functionals which enables a further generalization of the theory for continuous and discrete Sturm-Liouville equations.

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