Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1221.49040
Martins, Natália; Torres, Delfim F.M.
Generalizing the variational theory on time scales to include the delta indefinite integral. (English)
[J] Comput. Math. Appl. 61, No. 9, 2424-2435 (2011). ISSN 0898-1221

Summary: We prove necessary optimality conditions of Euler-Lagrange type for generalized problems of the calculus of variations on time scales with a Lagrangian depending not only on the independent variable, an unknown function and its delta derivative, but also on a delta indefinite integral that depends on the unknown function. Such kinds of variational problems were considered by Euler himself and have been recently investigated by {\it J. Gregory} [Methods Appl. Anal. 15, No. 4, 427--436 (2008; Zbl 1178.49024)]. Our results not only provide a generalization to previous results, but also give some other interesting optimality conditions as special cases.

MSC 2000:: *49K21
34A08

Keywords: time scales; calculus of variations; Euler-Lagrange equations; isoperimetric problems; natural boundary conditions

Citations: Zbl 1178.49024

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]