Double integral calculus of variations on time scales

Authors:
Martin Bohner;Gusein Sh. Guseinov
Affiliations:
University of Missouri-Rolla, Department of Mathematics and Statistics, Rolla, MO 65401, USA;Atilim University, Department of Mathematics, 06836 Incek, Ankara, Turkey
Venue:
Computers & Mathematics with Applications
Year:
2007

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Abstract

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.