A unified approach to the calculus of variations on time scales

摘要：

In this work we propose a new and more general approach to the calculus of variations on time scales that allows to obtain, as particular cases, both delta and nabla results. More precisely, we pose the problem of minimizing or maximizing the composition of delta and nabla integrals with Lagrangians that involve directional derivatives. Unified Euler-Lagrange necessary optimality conditions, as well as sufficient conditions under appropriate convexity assumptions, are proved. We illustrate presented results with simple examples.

关键词： Euler-Lagrange equations calculus of variations delta and nabla calculi time scales directional derivatives

作者: Ewa Girejko Agnieszka B. Malinowska Delfim F. M. Torres

作者单位: Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal Faculty of Computer Scien Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

会议类型: 国际会议

会议名称: The 22nd China Control and Decision Conference(2010年中国控制与决策会议)

会议地点: 徐州

会议语种:英文

页码: 595-600

在线出版日期: 2010-05-26（万方平台首次上网日期，不代表论文的发表时间）