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

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ZEMÁNEK Petr

Druh Článek v odborném periodiku
Časopis / Zdroj Applied Mathematics Letters
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
Doi http://dx.doi.org/10.1016/j.aml.2012.04.009
Obor Obecná matematika
Klíčová slova Time scale; even order Sturm-Liouville dynamic equation; time reversed symplectic system; quadratic functional
Popis 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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