Double integral calculus of variations on time scales

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Submitted to Computers and Mathematics with Applications DOUBLE INTEGRAL CALCULUS OF VARIATIONS ON TIME SCALES

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. AMS (MOS) Subject Classification. 39A0, 49K20.

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The calculus of variations is a classical subject which has gain throughout the last three hundred years a level of rigor and elegance that only time can give. In this note we show that, contrary to the classical field, available formulations and results on the recent calculus of variations on time scales are still at the heuristic level.

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Calculus of variations on time scales (we refer the reader to Section 2 for a brief introduction to time scales) has been introduced in 2004 in the papers by Bohner [2] and Hilscher and Zeidan [4], and seems to have many opportunities for application in economics [1]. In both works of Bohner and Hilscher&Zeidan, the Euler-Lagrange equation for the fundamental problem of the calculus of variatio...

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ژورنال

عنوان ژورنال: Computers & Mathematics with Applications

سال: 2007

ISSN: 0898-1221

DOI: 10.1016/j.camwa.2006.10.032