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AIMS Mathematics

2020, Volume 5, Issue 1: 111-139. doi: 10.3934/math.2020008
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Research article

Sufficiency for singular trajectories in the calculus of variations

  • Facultad de Ciencias, Universidad Nacional Autónoma de México, Departamento de Matemáticas, Ciudad de México 04510, México
  • Received: 25 July 2019 Accepted: 10 October 2019 Published: 23 October 2019

  • MSC : 49K15

  • For calculus of variations problems of Bolza with variable end-points, nonlinear inequality and equality isoperimetric constraints and nonlinear inequality and equality mixed pointwise constraints, sufficient conditions for strong minima are derived. The main novelty of the new sufficiency results presented in this article concerns their applicability to cases in which the derivatives of the extremals to be optimal solutions are not necessarily continuous nor piecewise continuous but only essentially bounded and they do not necessarily satisfy the standard strengthened Legendre condition but only the corresponding necessary condition.

    Citation: Gerardo Sánchez Licea. Sufficiency for singular trajectories in the calculus of variations[J]. AIMS Mathematics, 2020, 5(1): 111-139. doi: 10.3934/math.2020008

    Related Papers:

  • For calculus of variations problems of Bolza with variable end-points, nonlinear inequality and equality isoperimetric constraints and nonlinear inequality and equality mixed pointwise constraints, sufficient conditions for strong minima are derived. The main novelty of the new sufficiency results presented in this article concerns their applicability to cases in which the derivatives of the extremals to be optimal solutions are not necessarily continuous nor piecewise continuous but only essentially bounded and they do not necessarily satisfy the standard strengthened Legendre condition but only the corresponding necessary condition.


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    [13] A. A. Milyutin, N. P. Osmolovskii, Calculus of Variations and Optimal Control, Rhode Island: American Mathematical Society, 1998.
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