Detail publikace
A note on the equivalence between even order Sturm
-Liouville equations and symplectic systems on time scales
| Základní údaje | |
|---|---|
| Originální název: | A note on the equivalence between even order Sturm-Liouville equations and symplectic systems on time scales |
| Autor: | Petr Zemánek |
| Další údaje | |
|---|---|
| Citace: | ZEMÁNEK, Petr. A note on the equivalence between even order
Sturm-Liouville equations and symplectic systems on time
scales. Applied Mathematics Letters, USA: Elsevier, 2013, roč.
26, č. 1, s. 134-139. ISSN 0893-9659.
doi:10.1016/j.aml.2012.04.009.Export BibTeX @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} } |
| Originální jazyk: | angličtina |
| Obor: | Obecná matematika |
| Druh: | Článek v odborném periodiku |
| Klíčová slova: | 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.
Související projekty:
