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Volumn 276, Issue 1, 2002, Pages 396-421

Coupled intervals in the discrete calculus of variations: Necessity and sufficiency

Author keywords

Conjugate interval; Coupled interval; Discrete calculus of variations; Discrete quadratic functional; Jacobi difference equation; Legendre condition

Indexed keywords


EID: 0036948330     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(02)00495-X     Document Type: Article
Times cited : (11)

References (25)
  • 2
    • 0002928826 scopus 로고
    • Discrete variational inequalities
    • W. Walter (Ed.), General Inequalities 6, Proceedings of the 6th International Conference on General Inequalities, Oberwolfach, 1990, in: International Series of Numerical Mathematics, Birkhäuser, Basel
    • C.D. Ahlbrandt, Discrete variational inequalities, in: W. Walter (Ed.), General Inequalities 6, Proceedings of the 6th International Conference on General Inequalities, Oberwolfach, 1990, in: International Series of Numerical Mathematics, Vol. 123, Birkhäuser, Basel, 1992, pp. 93-107.
    • (1992) , vol.123 , pp. 93-107
    • Ahlbrandt, C.D.1
  • 3
    • 0002465359 scopus 로고    scopus 로고
    • Discrete Riccati equations of filtering and control
    • S. Elaydi, J. Graef, G. Ladas, A. Peterson (Eds.), Proceedings of the First International Conference on Difference Equations, San Antonio, TX, 1994, Gordon and Breach, Newark, NJ
    • C.D. Ahlbrandt, M. Heifetz, Discrete Riccati equations of filtering and control, in: S. Elaydi, J. Graef, G. Ladas, A. Peterson (Eds.), Proceedings of the First International Conference on Difference Equations, San Antonio, TX, 1994, Gordon and Breach, Newark, NJ, 1996, pp. 1-16.
    • (1996) , pp. 1-16
    • Ahlbrandt, C.D.1    Heifetz, M.2
  • 4
    • 0002811125 scopus 로고
    • A variational view of non-oscillation theory for linear difference equations
    • J.L. Henderson (Ed.), Proceedings of the Twelfth and Thirteenth Midwest Conferences, Iowa City, IO, 1983, Argonne, IL, 1984, Institute of Applied Mathematics, University of Missouri-Rolla, Rolla, MO
    • C.D. Ahlbrandt, J.W. Hooker, A variational view of non-oscillation theory for linear difference equations, in: J.L. Henderson (Ed.), Differential and Integral Equations, Proceedings of the Twelfth and Thirteenth Midwest Conferences, Iowa City, IO, 1983, Argonne, IL, 1984, Institute of Applied Mathematics, University of Missouri-Rolla, Rolla, MO, 1985, pp. 1-21.
    • (1985) Differential and Integral Equations , pp. 1-21
    • Ahlbrandt, C.D.1    Hooker, J.W.2
  • 5
    • 0003811971 scopus 로고    scopus 로고
    • Discrete Hamiltonian Systems: Difference Equations, Continued Fractions, and Riccati Equations
    • Kluwer Academic Publishers, Boston
    • C.D. Ahlbrandt, A.C. Peterson, Discrete Hamiltonian Systems: Difference Equations, Continued Fractions, and Riccati Equations, Kluwer Academic Publishers, Boston, 1996.
    • (1996)
    • Ahlbrandt, C.D.1    Peterson, A.C.2
  • 6
    • 0030147307 scopus 로고    scopus 로고
    • Linear Hamiltonian difference systems: Disconjugacy and Jacobi-type conditions
    • M. Bohner, Linear Hamiltonian difference systems: disconjugacy and Jacobi-type conditions, J. Math. Anal. Appl. 199 (1996) 804-826.
    • (1996) J. Math. Anal. Appl. , vol.199 , pp. 804-826
    • Bohner, M.1
  • 7
    • 0000613781 scopus 로고    scopus 로고
    • Riccati matrix difference equations and linear Hamiltonian difference systems
    • M. Bohner, Riccati matrix difference equations and linear Hamiltonian difference systems, Dynam. Contin. Discrete Impuls. Systems 2 (2) (1996) 147-159.
    • (1996) Dynam. Contin. Discrete Impuls. Systems , vol.2 , Issue.2 , pp. 147-159
    • Bohner, M.1
  • 8
    • 0038967596 scopus 로고    scopus 로고
    • Disconjugacy and transformations for symplectic systems
    • M. Bohner, O. Došlý, Disconjugacy and transformations for symplectic systems, Rocky Mountain J. Math. 27 (3) (1997) 707-743.
    • (1997) Rocky Mountain J. Math. , vol.27 , Issue.3 , pp. 707-743
    • Bohner, M.1    Došlý, O.2
  • 9
    • 0032217344 scopus 로고    scopus 로고
    • Positivity of block tridiagonal matrices
    • M. Bohner, O. Došlý, Positivity of block tridiagonal matrices, SIAM J. Matrix Anal. 20 (1) (1998) 182-195.
    • (1998) SIAM J. Matrix Anal. , vol.20 , Issue.1 , pp. 182-195
    • Bohner, M.1    Došlý, O.2
  • 11
    • 0031281613 scopus 로고    scopus 로고
    • Quadratic functionals with general boundary conditions
    • Z. Došlá, O. Došlý, Quadratic functionals with general boundary conditions, Appl. Math. Optim. 36 (1997) 243-262.
    • (1997) Appl. Math. Optim. , vol.36 , pp. 243-262
    • Došlá, Z.1    Došlý, O.2
  • 12
    • 0012567267 scopus 로고
    • Quadratic functionals with a variable singular end point
    • Z. Došlá, P. Zezza, Quadratic functionals with a variable singular end point, Comment. Math. Univ. Carolin. 33 (3) (1992) 411-425.
    • (1992) Comment. Math. Univ. Carolin. , vol.33 , Issue.3 , pp. 411-425
    • Došlá, Z.1    Zezza, P.2
  • 13
    • 0001341145 scopus 로고
    • Disconjugacy for linear Hamiltonian difference systems
    • L. Erbe, P. Yan, Disconjugacy for linear Hamiltonian difference systems, J. Math. Anal. Appl. 167 (1992) 355-367.
    • (1992) J. Math. Anal. Appl. , vol.167 , pp. 355-367
    • Erbe, L.1    Yan, P.2
  • 14
    • 38249008403 scopus 로고
    • Qualitative properties of Hamiltonian difference systems
    • L. Erbe, P. Yan, Qualitative properties of Hamiltonian difference systems, J. Math. Anal. Appl. 171 (1992) 334-345.
    • (1992) J. Math. Anal. Appl. , vol.171 , pp. 334-345
    • Erbe, L.1    Yan, P.2
  • 15
    • 0033473928 scopus 로고    scopus 로고
    • Disconjugacy of symplectic systems and positivity of block tridiagonal matrices
    • R. Hilscher, Disconjugacy of symplectic systems and positivity of block tridiagonal matrices, Rocky Mountain J. Math. 29 (4) (1999) 1301-1319.
    • (1999) Rocky Mountain J. Math. , vol.29 , Issue.4 , pp. 1301-1319
    • Hilscher, R.1
  • 16
    • 0001434067 scopus 로고    scopus 로고
    • Discrete optimal control: The accessory problem and necessary optimality conditions
    • R. Hilscher, V. Zeidan, Discrete optimal control: the accessory problem and necessary optimality conditions, J. Math. Anal. Appl. 243 (2) (2000) 429-452.
    • (2000) J. Math. Anal. Appl. , vol.243 , Issue.2 , pp. 429-452
    • Hilscher, R.1    Zeidan, V.2
  • 17
    • 0036000443 scopus 로고    scopus 로고
    • Second order sufficiency criteria for a discrete optimal control problem
    • R. Hilscher, V. Zeidan, Second order sufficiency criteria for a discrete optimal control problem, J. Differ. Equations Appl. 8 (6) (2002) 573-602.
    • (2002) J. Differ. Equations Appl. , vol.8 , Issue.6 , pp. 573-602
    • Hilscher, R.1    Zeidan, V.2
  • 18
    • 0012577049 scopus 로고    scopus 로고
    • Nonnegativity of a discrete quadratic functional in terms of the (strengthened) Legendre and Jacobi conditions
    • R.P. Agarwal (Ed.), Advances in Difference Equations IV to appear
    • R. Hilscher, V. Zeidan, Nonnegativity of a discrete quadratic functional in terms of the (strengthened) Legendre and Jacobi conditions, in: R.P. Agarwal (Ed.), Advances in Difference Equations IV, Comput. Math. Appl., to appear.
    • Comput. Math. Appl.
    • Hilscher, R.1    Zeidan, V.2
  • 20
    • 0031140637 scopus 로고    scopus 로고
    • Constrained regular LQ-control problems
    • G. Stefani, P. Zezza, Constrained regular LQ-control problems, SIAM J. Control Optim. 35 (3) (1997) 876-900.
    • (1997) SIAM J. Control Optim. , vol.35 , Issue.3 , pp. 876-900
    • Stefani, G.1    Zezza, P.2
  • 21
    • 0026754862 scopus 로고
    • Sufficiency criteria via focal points and via coupled points
    • V. Zeidan, Sufficiency criteria via focal points and via coupled points, SIAM J. Control Optim. 30 (1) (1992) 82-98.
    • (1992) SIAM J. Control Optim. , vol.30 , Issue.1 , pp. 82-98
    • Zeidan, V.1
  • 22
    • 0000423999 scopus 로고
    • Sufficient conditions for variational problems with variable endpoints: Coupled points
    • V. Zeidan, Sufficient conditions for variational problems with variable endpoints: coupled points, Appl. Math. Optim. 27 (2) (1993) 191-209.
    • (1993) Appl. Math. Optim. , vol.27 , Issue.2 , pp. 191-209
    • Zeidan, V.1
  • 23
    • 0000910491 scopus 로고    scopus 로고
    • Nonnegativity and positivity of a quadratic functional
    • R.P. Agarwal, M. Bohner (Eds.), Discrete and Continuous Hamiltonian Systems
    • V. Zeidan, Nonnegativity and positivity of a quadratic functional, in: R.P. Agarwal, M. Bohner (Eds.), Discrete and Continuous Hamiltonian Systems, Dynam. Systems Appl. 8 (3-4) (1999) 571-588.
    • (1999) Dynam. Systems Appl. , vol.8 , Issue.3-4 , pp. 571-588
    • Zeidan, V.1
  • 24
    • 0000317523 scopus 로고
    • Coupled points in the calculus of variations and applications to periodic problems
    • V Zeidan, P. Zezza, Coupled points in the calculus of variations and applications to periodic problems, Trans. Amer. Math. Soc. 315 (1) (1989) 323-335.
    • (1989) Trans. Amer. Math. Soc. , vol.315 , Issue.1 , pp. 323-335
    • Zeidan, V.1    Zezza, P.2
  • 25
    • 0027542403 scopus 로고
    • Jacobi condition for elliptic forms in Hilbert spaces
    • P. Zezza, Jacobi condition for elliptic forms in Hilbert spaces, J. Optim. Theory Appl. 76 (2) (1993) 357-380.
    • (1993) J. Optim. Theory Appl. , vol.76 , Issue.2 , pp. 357-380
    • Zezza, P.1


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