Open AccessMathematics

Agnieszka B. Malinowska, Delfim F. M. Torres

2009.5.1PROCEEDINGS OF THE ESTONIAN ACADEMY OF SCIENCES

DOI: 10.3176/proc.2009.4.02

tlooto Summary

Strong minimizers of the calculus of variations on time scales and the Weierstrass condition are introduced, enabling generalization to both continuous-time and discrete-time conditions.

Abstract

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.

Citation format

MALINOWSKA, Agnieszka B.; TORRES, Delfim F. M. Strong minimizers of the calculus of variations on time scales and the weierstrass condition [preprint]. arXiv, 2009. arXiv:0905.1870.