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arXiv · 1102.3727

Generalizing the variational theory on time scales to include the delta indefinite integral

Natalia Martins·Delfim F. M. Torres
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Abstract

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 kind of variational problems were considered by Euler himself and have been recently investigated in [Methods Appl. Anal. 15 (2008), no. 4, 427-435]. Our results not only provide a generalization to previous results, but also give some other interesting optimality conditions as special cases.

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Natalia Martins, Delfim F. M. Torres. 2011-02-18. Generalizing the variational theory on time scales to include the delta indefinite integral. https://doi.org/10.1016/j.camwa.2011.02.022

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