Strong minimizers of the calculus of variations on time scales and the Weierstr...

• Author(s): Malinowska, A.B. ; Torres, D.F.M.
• Date: 2009
• Persistent ID: http://hdl.handle.net/10773/4083
• Origin: RIA - Repositório Institucional da Universidade de Aveiro
• Subject(s): Calculus of variations; Strong minimizers; Time scales; Weierstrass optimality condition
• Document Type: Article
• Language: English

Description

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.