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.
G. S. Guseinov and M. Bohner, "Double Integral Calculus of Variations on Time Scales," Computers and Mathematics with Applications, Pergamon Press (Elsevier), Jul 2007.
The definitive version is available at http://dx.doi.org/10.1016/j.camwa.2006.10.032
Mathematics and Statistics
Keywords and Phrases
Double Delta Integrals; Euler-Lagrange Equation; Partial Delta Derivatives; Time Scales
Article - Journal
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