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

作者：Zemanek Petr^*

来源：Applied Mathematics Letters, 2013, 26(1): 134-139.

DOI：10.1016/j.aml.2012.04.009

• Time scale
• Even order Sturm-Liouville dynamic equation
• Time reversed symplectic system
• Quadratic functional

The 2nth-order Sturm-Liouville differential and difference equations can be written as linear Hamiltonian differential systems and symplectic difference systems, respectively. In this work, a similar result is given for the 2nth-order Sturm-Liouville equation on time scales 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.

• 出版日期2013-1