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Double integral calculus of variations on time scales

✍ Scribed by Martin Bohner; Gusein Sh. Guseinov

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
286 KB
Volume
54
Category
Article
ISSN
0898-1221

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✦ Synopsis

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 them an analogue of the Euler-Lagrange equation.

πŸ“œ SIMILAR VOLUMES

Calculus of variations on time scales wi
Calculus of variations on time scales with nabla derivatives
✍ NatΓ‘lia Martins; Delfim F.M. Torres πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 327 KB

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.

Generalized double-integral Ostrowski ty
Generalized double-integral Ostrowski type inequalities on time scales
✍ Sabir Hussain; Muhammad Amer Latif; Mohammad Alomari πŸ“‚ Article πŸ“… 2011 πŸ› Elsevier Science 🌐 English βš– 234 KB

An Ostrowski type inequality for a double integral is derived via a βˆ†βˆ†-integral on time scales; this generalizes an Ostrowski type inequality and some related results from Liu et al. ( 2010) [1]. Some new applications are also given.