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Volumn 24, Issue 1, 2011, Pages 87-92

Optimality conditions for the calculus of variations with higher-order delta derivatives

Author keywords

Arbitrary time scales; Calculus of variations; EulerLagrange equation; Higher order delta derivatives

Indexed keywords

ARBITRARY TIME; CALCULUS OF VARIATIONS; EULER-LAGRANGE; EULERLAGRANGE EQUATION; HIGHER ORDER; INTEGRAL FUNCTIONALS; OPTIMALITY CONDITIONS;

EID: 77957553198     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2010.08.023     Document Type: Article
Times cited : (28)

References (26)
  • 1
    • 77953586739 scopus 로고    scopus 로고
    • Integral inequalities and their applications to the calculus of variations on time scales
    • M. Bohner, R.A.C. Ferreira, and D.F.M. Torres Integral inequalities and their applications to the calculus of variations on time scales Math. Inequal. Appl. 13 3 2010 511-522
    • (2010) Math. Inequal. Appl. , vol.13 , Issue.3 , pp. 511-522
    • Bohner, M.1    Ferreira, R.A.C.2    Torres, D.F.M.3
  • 2
    • 84856931004 scopus 로고    scopus 로고
    • The contingent epiderivative and the calculus of variations on time scales
    • in press (doi:10.1080/02331934.2010.506615)
    • E. Girejko, A.B. Malinowska, D.F.M. Torres, The contingent epiderivative and the calculus of variations on time scales, Optimization (2010), in press (doi:10.1080/02331934.2010.506615 ).
    • (2010) Optimization
    • Girejko, E.1    Malinowska, A.B.2    Torres, D.F.M.3
  • 4
    • 78650756398 scopus 로고    scopus 로고
    • Transversality conditions for infinite horizon variational problems on time scales
    • in press (doi:10.1007/s11590-010-0189-7)
    • A.B. Malinowska, N. Martins, D.F.M. Torres, Transversality conditions for infinite horizon variational problems on time scales, Optim. Lett. (2010), in press (doi:10.1007/s11590-010-0189-7 ).
    • (2010) Optim. Lett.
    • Malinowska, A.B.1    Martins, N.2    Torres, D.F.M.3
  • 5
    • 77956920358 scopus 로고    scopus 로고
    • Natural boundary conditions in the calculus of variations
    • (in press). doi:10.1002/mma.1289
    • A.B. Malinowska, D.F.M. Torres, Natural boundary conditions in the calculus of variations, Math. Methods Appl. Sci. (2010) (in press) doi:10.1002/mma.1289.
    • (2010) Math. Methods Appl. Sci.
    • Malinowska, A.B.1    Torres, D.F.M.2
  • 6
    • 77957284778 scopus 로고    scopus 로고
    • Leitmann's direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales
    • in press (doi:10.1016/j.amc.2010.01.015)
    • A.B. Malinowska, D.F.M. Torres, Leitmann's direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales, Appl. Math. Comput. (2010), in press (doi:10.1016/j.amc.2010.01.015 ).
    • (2010) Appl. Math. Comput.
    • Malinowska, A.B.1    Torres, D.F.M.2
  • 7
    • 78049392558 scopus 로고    scopus 로고
    • The Hahn quantum variational calculus
    • in press (doi:10.1007/s10957-010-9730-1)
    • A.B. Malinowska, D.F.M. Torres, The Hahn quantum variational calculus, J. Optim. Theory Appl. 147 3 (2010), in press (doi:10.1007/s10957-010-9730-1 ).
    • (2010) J. Optim. Theory Appl. , vol.147 , Issue.3
    • Malinowska, A.B.1    Torres, D.F.M.2
  • 8
    • 80052965275 scopus 로고    scopus 로고
    • A general backwards calculus of variations via duality
    • in press (doi:10.1007/s11590-010-0222-x)
    • A.B. Malinowska, D.F.M. Torres, A general backwards calculus of variations via duality, Optim. Lett. (2010), in press (doi:10.1007/s11590-010- 0222-x ).
    • (2010) Optim. Lett.
    • Malinowska, A.B.1    Torres, D.F.M.2
  • 9
    • 77957579664 scopus 로고    scopus 로고
    • Noether's symmetry theorem for nabla problems of the calculus of variations
    • in press (doi:10.1016/j.aml.2010.07.013)
    • N. Martins, D.F.M. Torres, Noether's symmetry theorem for nabla problems of the calculus of variations, Appl. Math. Lett. (2010), in press (doi:10.1016/j.aml.2010.07.013 ).
    • (2010) Appl. Math. Lett.
    • Martins, N.1    Torres, D.F.M.2
  • 10
    • 66249145058 scopus 로고    scopus 로고
    • Isoperimetric problems on time scales with nabla derivatives
    • R. Almeida, and D.F.M. Torres Isoperimetric problems on time scales with nabla derivatives J. Vib. Control 15 6 2009 951-958
    • (2009) J. Vib. Control , vol.15 , Issue.6 , pp. 951-958
    • Almeida, R.1    Torres, D.F.M.2
  • 12
    • 63649096585 scopus 로고    scopus 로고
    • A comparison in the theory of calculus of variations on time scales with an application to the Ramsey model
    • F.M. Atici, and C.S. McMahan A comparison in the theory of calculus of variations on time scales with an application to the Ramsey model Nonlinear Dyn. Syst. Theory 9 1 2009 1-10
    • (2009) Nonlinear Dyn. Syst. Theory , vol.9 , Issue.1 , pp. 1-10
    • Atici, F.M.1    McMahan, C.S.2
  • 14
    • 12844271148 scopus 로고    scopus 로고
    • Calculus of variations on time scales
    • M. Bohner Calculus of variations on time scales Dynam. Systems Appl. 13 34 2004 339-349
    • (2004) Dynam. Systems Appl. , vol.13 , Issue.34 , pp. 339-349
    • Bohner, M.1
  • 15
    • 40649083669 scopus 로고    scopus 로고
    • Remarks on the calculus of variations on time scales
    • R.A.C. Ferreira, and D.F.M. Torres Remarks on the calculus of variations on time scales Int. J. Ecol. Econ. Stat. 9 F07 2007 65-73
    • (2007) Int. J. Ecol. Econ. Stat. , vol.9 , Issue.F07 , pp. 65-73
    • Ferreira, R.A.C.1    Torres, D.F.M.2
  • 17
    • 0346946902 scopus 로고    scopus 로고
    • Calculus of variations on time scales: Weak local piecewise Crd1 solutions with variable endpoints
    • R. Hilscher, and V. Zeidan Calculus of variations on time scales: weak local piecewise C rd 1 solutions with variable endpoints J. Math. Anal. Appl. 289 1 2004 143-166
    • (2004) J. Math. Anal. Appl. , vol.289 , Issue.1 , pp. 143-166
    • Hilscher, R.1    Zeidan, V.2
  • 18
    • 70350302594 scopus 로고    scopus 로고
    • Necessary and sufficient conditions for local Pareto optimality on time scales
    • A.B. Malinowska, and D.F.M. Torres Necessary and sufficient conditions for local Pareto optimality on time scales J. Math. Sci. (N.Y.) 161 6 2009 803-810
    • (2009) J. Math. Sci. (N.Y.) , vol.161 , Issue.6 , pp. 803-810
    • Malinowska, A.B.1    Torres, D.F.M.2
  • 19
    • 73649140946 scopus 로고    scopus 로고
    • Strong minimizers of the calculus of variations on time scales and the Weierstrass condition
    • A.B. Malinowska, and D.F.M. Torres Strong minimizers of the calculus of variations on time scales and the Weierstrass condition Proc. Est. Acad. Sci. 58 4 2009 205-212
    • (2009) Proc. Est. Acad. Sci. , vol.58 , Issue.4 , pp. 205-212
    • Malinowska, A.B.1    Torres, D.F.M.2
  • 21
    • 72149132561 scopus 로고    scopus 로고
    • Calculus of variations on time scales with nabla derivatives
    • N. Martins, and D.F.M. Torres Calculus of variations on time scales with nabla derivatives Nonlinear Anal. 71 12 2009 e763-e773
    • (2009) Nonlinear Anal. , vol.71 , Issue.12
    • Martins, N.1    Torres, D.F.M.2
  • 24
    • 84951604495 scopus 로고
    • Analysis on measure chainsa unified approach to continuous and discrete calculus
    • S. Hilger Analysis on measure chainsa unified approach to continuous and discrete calculus Results Math. 18 12 1990 18-56
    • (1990) Results Math. , vol.18 , Issue.12 , pp. 18-56
    • Hilger, S.1
  • 25
    • 0001028781 scopus 로고    scopus 로고
    • Differential and difference calculusunified!
    • S. Hilger Differential and difference calculusunified! Nonlinear Anal. 30 5 1997 2683-2694
    • (1997) Nonlinear Anal. , vol.30 , Issue.5 , pp. 2683-2694
    • Hilger, S.1
  • 26
    • 61349150026 scopus 로고    scopus 로고
    • Weak maximum principle and accessory problem for control problems on time scales
    • R. Hilscher, and V. Zeidan Weak maximum principle and accessory problem for control problems on time scales Nonlinear Anal. 70 9 2009 3209-3226
    • (2009) Nonlinear Anal. , vol.70 , Issue.9 , pp. 3209-3226
    • Hilscher, R.1    Zeidan, V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.