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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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Original title:A note on the equivalence between even order Sturm-Liouville equations and symplectic systems on time scales
Author:Petr Zemánek
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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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