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Higher-Order Variational Problems of Herglotz Type


We obtain a generalized Euler–Lagrange differential equation and transversality optimality conditions for Herglotz-type higher-order variational problems. Illustrative examples of the new results are given.

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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 the FCT project PTDC/EEI-AUT/1450/2012, co-financed by FEDER under POFC-QREN with COMPETE reference FCOMP-01-0124-FEDER-028894. The authors are grateful to two anonymous referees for their valuable comments and helpful suggestions.

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Correspondence to Delfim F. M. Torres.

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Dedicated to Boris Mordukhovich on the occasion of his 65th Birthday.

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Santos, S.P.S., Martins, N. & Torres, D.F.M. Higher-Order Variational Problems of Herglotz Type. Vietnam J. Math. 42, 409–419 (2014).

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  • Euler–Lagrange differential equations
  • Natural boundary conditions
  • Generalized calculus of variations

Mathematics Subject Classification (2010)

  • 34H05
  • 49K15