Journal of Optimization Theory and Applications

, Volume 155, Issue 2, pp 453–476 | Cite as

Necessary Optimality Conditions for Higher-Order Infinite Horizon Variational Problems on Time Scales

  • Natália Martins
  • Delfim F. M. Torres


We obtain Euler–Lagrange and transversality optimality conditions for higher-order infinite horizon variational problems on a time scale. The new necessary optimality conditions improve the classical results both in the continuous and discrete settings: Our results seem new and interesting even in the particular cases when the time scale is the set of real numbers or the set of integers.


Time scales Calculus of variations Infinite horizon problems Euler–Lagrange equations Transversality conditions 



This work was supported by FEDER funds through COMPETE—Operational Programme Factors of Competitiveness (“Programa Operacional Factores de Competitividade”) and by Portuguese funds through the Center for Research and Development in Mathematics and Applications (University of Aveiro) and the Portuguese Foundation for Science and Technology (“FCT—Fundação para a Ciência e a Tecnologia”), within project PEst-C/MAT/UI4106/2011 with COMPETE number FCOMP-01-0124-FEDER-022690. Torres was also supported by project PTDC/MAT/113470/2009.


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of AveiroAveiroPortugal
  2. 2.Research Group on Mathematical Theory of Systems and Control, Center for Research and Development in Mathematics and Applications, Department of MathematicsUniversity of AveiroAveiroPortugal

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