Double Integral Calculus of Variations on Time Scales

Gusein Sh. Guseinov
Martin Bohner, Missouri University of Science and Technology

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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.