We consider a version of the double integral calculus of variations on time scales, which includes as special cases the classical two-variable calculus of variations and the discrete two-variable calculus of variations. Necessary and sufficient conditions for a local extremum are established, among
Basics of diamond- partial dynamic calculus on time scales
✍ Scribed by Umut Mutlu Özkan; Billûr Kaymakçalan
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 566 KB
- Volume
- 50
- Category
- Article
- ISSN
- 0895-7177
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📜 SIMILAR VOLUMES
We prove a necessary optimality condition of the Euler-Lagrange type for variational problems on time scales involving nabla derivatives of higher order. The proof is done using a new and more general fundamental lemma of the calculus of variations on time scales.
Interval oscillation criteria are established for a second-order nonlinear dynamic equation on time scales by utilizing a generalized Riccati technique and the Young inequality. The theory can be applied to second-order dynamic equations regardless of the choice of delta or nabla derivatives.