Abstract:The aim of this paper is to introduce the definition of coupled points for the problems of the calculus of variations with general boundary conditions, and to develop second order necessary conditions for optimality. When one of the end points is fixed, our necessary conditions reduce to the known ones involving conjugate points. We also apply our results to the periodic problems of the calculus of variations.
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- © Copyright 1989 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 315 (1989), 323-335
- MSC: Primary 49B21; Secondary 49D50
- DOI: https://doi.org/10.1090/S0002-9947-1989-0961599-X
- MathSciNet review: 961599