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Strong minimizers of the calculus of variations on time scales and the Weierstrass condition. (English) Zbl 1179.49025

Summary: We introduce the notion of strong local minimizer for the problems of the calculus of variations on time scales. Simple examples show that on a time scale a weak minimum is not necessarily a strong minimum. A time scale form of the Weierstrass necessary optimality condition is proved, which enables to include and generalize in the same result both continuous-time and discrete-time conditions.

MSC:

49K15 Optimality conditions for problems involving ordinary differential equations
34N05 Dynamic equations on time scales or measure chains
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