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  • 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.
  • 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. (en)
Title
  • A note on the equivalence between even order Sturm-Liouville equations and symplectic systems on time scales
  • A note on the equivalence between even order Sturm-Liouville equations and symplectic systems on time scales (en)
skos:prefLabel
  • A note on the equivalence between even order Sturm-Liouville equations and symplectic systems on time scales
  • A note on the equivalence between even order Sturm-Liouville equations and symplectic systems on time scales (en)
skos:notation
  • RIV/00216224:14310/13:00065916!RIV14-GA0-14310___
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  • P(GAP201/10/1032)
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  • RIV/00216224:14310/13:00065916
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  • Time scale; even order Sturm-Liouville dynamic equation; time reversed symplectic system; quadratic functional (en)
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  • US - Spojené státy americké
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  • [2032C5E992EF]
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  • Applied Mathematics Letters
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  • 26
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  • Zemánek, Petr
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  • 000309300800026
issn
  • 0893-9659
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  • 10.1016/j.aml.2012.04.009
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  • 14310
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