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

• Autoři: ZEMÁNEK Petr
• Rok publikování: 2013
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Applied Mathematics Letters
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• Doi: https://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

Přiložené soubory

• A_note_on_the_equivalence_between_even_order_Sturm-Liouville_equations_and_symplectic_systems_on_time_scales__PDF_Offprint__Zemanek_.pdf

• 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.

Související projekty

• Diferenční rovnice a dynamické rovnice na time scales III