A note on the equivalence between even order Sturm-Liouville equations and symplectic systems on time scales
| Authors | |
|---|---|
| Year of publication | 2013 |
| Type | Article in Periodical |
| Magazine / Source | Applied Mathematics Letters |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1016/j.aml.2012.04.009 |
| Field | General mathematics |
| Keywords | Time scale; even order Sturm-Liouville dynamic equation; time reversed symplectic system; quadratic functional |
| Attached files | |
| Description | 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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