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@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} }
TY - JOUR ID - 979812 AU - Zemánek, Petr PY - 2013 TI - A note on the equivalence between even order Sturm-Liouville equations and symplectic systems on time scales JF - Applied Mathematics Letters VL - 26 IS - 1 SP - 134-139 EP - 134-139 PB - Elsevier SN - 08939659 KW - Time scale KW - even order Sturm-Liouville dynamic equation KW - time reversed symplectic system KW - quadratic functional N2 - 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. ER -
ZEMÁNEK, Petr. A note on the equivalence between even order Sturm-Liouville equations and symplectic systems on time scales. \textit{Applied Mathematics Letters}. USA: Elsevier, roč.~26, č.~1, s.~134-139. ISSN~0893-9659. doi:10.1016/j.aml.2012.04.009. 2013.
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