A note on the equivalence between even order Sturm-Liouville equations and symplectic systems on time scales
|Original title:||A note on the equivalence between even order Sturm-Liouville equations and symplectic systems on time scales|
|Type:||Article in Periodical|
|Keywords:||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.