Necessary Condition for an Euler-Lagrange Equation on Time Scales

被引：1
作者：
Dryl, Monika [1 ]
Torres, Delfim F. M. [1 ]
机构：
[1] Univ Aveiro, Dept Math, Ctr Res & Dev Math & Applicat CIDMA, P-3810193 Aveiro, Portugal
来源：
ABSTRACT AND APPLIED ANALYSIS | 2014年
关键词：
VARIATIONAL-PROBLEMS; NABLA DERIVATIVES; CALCULUS;
D O I：
10.1155/2014/631281
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove a necessary condition for a dynamic integrodifferential equation to be an Euler-Lagrange equation. New and interesting results for the discrete and quantum calculus are obtained as particular cases. An example of a second order dynamic equation, which is not an Euler-Lagrange equation on an arbitrary time scale, is given.
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页数：7
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共 21 条
  • [1] Dynamic equations on time scales: a survey
    Agarwal, R
    Bohner, M
    O'Regan, D
    Peterson, A
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2002, 141 (1-2) : 1 - 26
  • [2] Isoperimetric Problems on Time Scales with Nabla Derivatives
    Almeida, Ricardo
    Torres, Delfim F. M.
    [J]. JOURNAL OF VIBRATION AND CONTROL, 2009, 15 (06) : 951 - 958
  • [3] Discrete-time fractional variational problems
    Bastos, Nuno R. O.
    Ferreira, Rui A. C.
    Torres, Delfim F. M.
    [J]. SIGNAL PROCESSING, 2011, 91 (03) : 513 - 524
  • [4] Bohner M., 2001, Dynamic Equations on Time Scales: An Introduction with Applications, DOI DOI 10.1007/978-1-4612-0201-1
  • [5] Bohner M., 2003, Advances in Dynamic Equations on Time Scales, DOI DOI 10.1007/978-0-8176-8230-9
  • [6] Helmholtz's inverse problem of the discrete calculus of variations
    Bourdin, Loic
    Cresson, Jacky
    [J]. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2013, 19 (09) : 1417 - 1436
  • [7] PONTRYAGIN MAXIMUM PRINCIPLE FOR FINITE DIMENSIONAL NONLINEAR OPTIMAL CONTROL PROBLEMS ON TIME SCALES
    Bourdin, Loiec
    Trelat, Emmanuel
    [J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2013, 51 (05) : 3781 - 3813
  • [8] Time scale differential, integral, and variational embeddings of Lagrangian systems
    Cresson, Jacky
    Malinowska, Agnieszka B.
    Torres, Delfim F. M.
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2012, 64 (07) : 2294 - 2301
  • [9] Davis DR, 1928, T AM MATH SOC, V30, P710
  • [10] Dryl Monika, 2013, Control and Cybernetics, V42, P399
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