Malinowska, Agnieszka B.; Torres, Delfim F. M. Strong minimizers of the calculus of variations on time scales and the Weierstrass condition. (English) Zbl 1179.49025 Proc. Est. Acad. Sci. 58, No. 4, 205-212 (2009). 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. Cited in 17 Documents MSC: 49K15 Optimality conditions for problems involving ordinary differential equations 34N05 Dynamic equations on time scales or measure chains Keywords:calculus of variations; time scales; strong minimizers; Weierstrass optimality condition PDFBibTeX XMLCite \textit{A. B. Malinowska} and \textit{D. F. M. Torres}, Proc. Est. Acad. Sci. 58, No. 4, 205--212 (2009; Zbl 1179.49025) Full Text: DOI arXiv