The Variational Calculus on Time Scales

DOI10.1051/IJSMDO/2010003arXiv1106.3597MaRDI QIDQ6226085

Publication date: 17 June 2011

Abstract: The discrete, the quantum, and the continuous calculus of variations, have been recently unified and extended by using the theory of time scales. Such unification and extension is, however, not unique, and two approaches are followed in the literature: one dealing with minimization of delta integrals; the other dealing with minimization of nabla integrals. Here we review a more general approach to the calculus of variations on time scales that allows to obtain both delta and nabla results as particular cases.

Mathematics Subject Classification ID

Discrete version of topics in analysis (39A12) Optimality conditions for free problems in one independent variable (49K05) Dynamic equations on time scales or measure chains (34N05)

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