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Volumn 43, Issue 2, 2001, Pages 129-146

Reid Roundabout Theorem for Symplectic Dynamic Systems on Time Scales

Author keywords

Disconjugacy; Focal point; Jacobi condition; Legendre condition; Linear Hamiltonian system; Principal solution; Quadratic functional; Riccati equation; Symplectic system; Time scale

Indexed keywords

BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; EQUIVALENCE CLASSES; HAMILTONIANS; MATRIX ALGEBRA; PROBLEM SOLVING; RICCATI EQUATIONS; VECTORS;

EID: 0000226297     PISSN: 00954616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00245-001-0002-1     Document Type: Article
Times cited : (26)

References (46)
  • 1
    • 0032166412 scopus 로고    scopus 로고
    • Quadratic functionals for second order matrix equations on time scales
    • Agarwal RP, Bohner M (1998) Quadratic functionals for second order matrix equations on time scales. Nonlinear Anal 33(7):675-692
    • (1998) Nonlinear Anal , vol.33 , Issue.7 , pp. 675-692
    • Agarwal, R.P.1    Bohner, M.2
  • 2
    • 0000990742 scopus 로고    scopus 로고
    • Sturm-Liouville eigenvalue problems on time scales
    • Agarwal RP, Bohner M, Wong PJY (1999) Sturm-Liouville eigenvalue problems on time scales. Appl Math Comput 99:153-166
    • (1999) Appl Math Comput , vol.99 , pp. 153-166
    • Agarwal, R.P.1    Bohner, M.2    Wong, P.J.Y.3
  • 3
    • 0002928826 scopus 로고
    • Discrete variational inequalities
    • General Inequalities 6, Proceedings of the 6th International Conference on General Inequalities (Oberwolfach, 1990), Walter W, editor. Birkhäuser Verlag, Basel
    • Ahlbrandt CD (1992) Discrete variational inequalities. In General Inequalities 6, Proceedings of the 6th International Conference on General Inequalities (Oberwolfach, 1990), Walter W, editor. International Series of Numerical Mathematics, vol 123, pp 93-107. Birkhäuser Verlag, Basel
    • (1992) International Series of Numerical Mathematics , vol.123 , pp. 93-107
    • Ahlbrandt, C.D.1
  • 4
    • 0000964386 scopus 로고
    • Equivalence of discrete Euler equations and discrete Hamiltonian systems
    • Ahlbrandt CD (1993) Equivalence of discrete Euler equations and discrete Hamiltonian systems. J Math Anal Appl 180:498-517
    • (1993) J Math Anal Appl , vol.180 , pp. 498-517
    • Ahlbrandt, C.D.1
  • 6
    • 0002104807 scopus 로고
    • A discrete interpretation of Reid's roundabout theorem for generalized differential systems
    • Ahlbrandt CD, Clark SL, Hooker JW, Patula WT (1994) A discrete interpretation of Reid's roundabout theorem for generalized differential systems. Comput Math Appl 28(1-3):11-21
    • (1994) Comput Math Appl , vol.28 , Issue.1-3 , pp. 11-21
    • Ahlbrandt, C.D.1    Clark, S.L.2    Hooker, J.W.3    Patula, W.T.4
  • 7
    • 0002465359 scopus 로고    scopus 로고
    • Discrete Riccati equations of filtering and control
    • (San Antonio, TX, 1994), Elaydi S, Graef J, Ladas G, Peterson A, editors, Gordon and Breach. Newark, NJ
    • Ahlbrandt CD, Heifetz M (1996) Discrete Riccati equations of filtering and control. In Proceedings of the First International Conference on Difference Equations (San Antonio, TX, 1994), Elaydi S, Graef J, Ladas G, Peterson A, editors, pp 1-16. Gordon and Breach. Newark, NJ
    • (1996) Proceedings of the First International Conference on Difference Equations , pp. 1-16
    • Ahlbrandt, C.D.1    Heifetz, M.2
  • 8
    • 0002811125 scopus 로고
    • A variational view of nonoscillation theory for linear difference equations
    • Proceedings of the Twelfth and Thirteenth Midwest Conferences (Argonne, IL, 1984), Henderson JL, editor, Institute of Applied Mathematics, University of Missouri-Rolla, Rolla, MO
    • Ahlbrandt CD, Hooker JW (1985) A variational view of nonoscillation theory for linear difference equations. In Differential and Integral Equations, Proceedings of the Twelfth and Thirteenth Midwest Conferences (Argonne, IL, 1984), Henderson JL, editor, pp 1-21. Institute of Applied Mathematics, University of Missouri-Rolla, Rolla, MO
    • (1985) Differential and Integral Equations , pp. 1-21
    • Ahlbrandt, C.D.1    Hooker, J.W.2
  • 9
    • 0242529970 scopus 로고
    • Disconjugacy criteria for second order linear difference equations
    • Proceedings of the 1984 Edmonton Conference Alegretto W, Butler GJ, editors
    • Ahlbrandt CD, Hooker JW (1986) Disconjugacy criteria for second order linear difference equations. In Qualitative Properties of Differential Equations. Proceedings of the 1984 Edmonton Conference. Alegretto W, Butler GJ, editors, pp 15-26
    • (1986) Qualitative Properties of Differential Equations , pp. 15-26
    • Ahlbrandt, C.D.1    Hooker, J.W.2
  • 10
    • 0002036279 scopus 로고
    • Recessive solutions of three term recurrence relations
    • (Toronto, 1986) Atkinson F, Langford W, Mingarelli A, editors, Canadian Mathematical Society Conference Proceedings, American Mathematical Society, Providence, RI
    • Ahlbrandt CD, Hooker JW (1987) Recessive solutions of three term recurrence relations. In Oscillations, Bifurcation and Chaos (Toronto, 1986) Atkinson F, Langford W, Mingarelli A, editors, pp 3-42. Canadian Mathematical Society Conference Proceedings, vol 8. American Mathematical Society, Providence, RI
    • (1987) Oscillations, Bifurcation and Chaos , vol.8 , pp. 3-42
    • Ahlbrandt, C.D.1    Hooker, J.W.2
  • 11
    • 0000192937 scopus 로고
    • Riccati matrix difference equations and disconjugacy of discrete linear systems
    • Ahlbrandt CD, Hooker JW (1988) Riccati matrix difference equations and disconjugacy of discrete linear systems. SIAM J Math Anal 19(5): 1183-1197
    • (1988) SIAM J Math Anal , vol.19 , Issue.5 , pp. 1183-1197
    • Ahlbrandt, C.D.1    Hooker, J.W.2
  • 14
    • 0242614601 scopus 로고
    • A unified approach to continuous and discrete dynamics
    • (Szeged, 1988), Colloquia Mathematica Societatis János Bolyai, 53. North-Holland, Amsterdam
    • Aulbach B, Hilger S (1990) A unified approach to continuous and discrete dynamics. In Qualitative Theory of Differential Equations (Szeged, 1988), pp 37-56. Colloquia Mathematica Societatis János Bolyai, 53. North-Holland, Amsterdam
    • (1990) Qualitative Theory of Differential Equations , pp. 37-56
    • Aulbach, B.1    Hilger, S.2
  • 16
    • 0030147307 scopus 로고    scopus 로고
    • Linear Hamiltonian difference systems: Disconjugacy and Jacobi-type conditions
    • Bohner M (1996) Linear Hamiltonian difference systems: disconjugacy and Jacobi-type conditions. J Math Anal Appl 199:804-826
    • (1996) J Math Anal Appl , vol.199 , pp. 804-826
    • Bohner, M.1
  • 17
    • 0000613781 scopus 로고    scopus 로고
    • Riccati matrix difference equations and linear Hamiltonian difference systems
    • Bohner M (1996) Riccati matrix difference equations and linear Hamiltonian difference systems. Dynam Contin Discrete Impuls Systems 2(2):147-159
    • (1996) Dynam Contin Discrete Impuls Systems , vol.2 , Issue.2 , pp. 147-159
    • Bohner, M.1
  • 18
    • 0000141815 scopus 로고    scopus 로고
    • On disconjugacy for Sturm-Liouville difference equations
    • Bohner M (1996) On disconjugacy for Sturm-Liouville difference equations. J Differ Equations Appl 2(2):227-237
    • (1996) J Differ Equations Appl , vol.2 , Issue.2 , pp. 227-237
    • Bohner, M.1
  • 19
    • 0040792832 scopus 로고    scopus 로고
    • Symplectic systems and related discrete quadratic functionals
    • Bohner M (1997) Symplectic systems and related discrete quadratic functionals. Facta Univ Ser Math Inform 12:143-156
    • (1997) Facta Univ Ser Math Inform , vol.12 , pp. 143-156
    • Bohner, M.1
  • 20
    • 0010749912 scopus 로고    scopus 로고
    • Inhomogeneous discrete variational problems
    • Proceedings of the Second International Conference on Difference Equations (Veszprem, 1995), Elaydi S, Györi I, and Ladas G, editors, Gordon and Breach, Amsterdam
    • Bohner M (1997) Inhomogeneous discrete variational problems. In Advances in Difference Equations, Proceedings of the Second International Conference on Difference Equations (Veszprem, 1995), Elaydi S, Györi I, and Ladas G, editors, pp 89-97. Gordon and Breach, Amsterdam
    • (1997) Advances in Difference Equations , pp. 89-97
    • Bohner, M.1
  • 21
    • 0038967596 scopus 로고    scopus 로고
    • Disconjugacy and transformations for symplectic systems
    • Bohner M, Došlý O (1997) Disconjugacy and transformations for symplectic systems. Rocky Mountain J Math 27(3):707-743
    • (1997) Rocky Mountain J Math , vol.27 , Issue.3 , pp. 707-743
    • Bohner, M.1    Došlý, O.2
  • 22
    • 0034629688 scopus 로고    scopus 로고
    • Trigonometric transformation of symplectic difference systems
    • Bohner M, Došlý O (2000) Trigonometric transformation of symplectic difference systems. J Differential Equations 163(1):113-129
    • (2000) J Differential Equations , vol.163 , Issue.1 , pp. 113-129
    • Bohner, M.1    Došlý, O.2
  • 23
  • 24
    • 0001742539 scopus 로고    scopus 로고
    • A Sturmian theorem for recessive solutions of linear Hamiltonian difference systems
    • Bohner M, Došlý O, Kratz W (1999) A Sturmian theorem for recessive solutions of linear Hamiltonian difference systems. Appl Math Lett 12:101-106
    • (1999) Appl Math Lett , vol.12 , pp. 101-106
    • Bohner, M.1    Došlý, O.2    Kratz, W.3
  • 27
    • 0031281613 scopus 로고    scopus 로고
    • Quadratic functionals with general boundary conditions
    • Došlá Z, Došlý O (1997) Quadratic functionals with general boundary conditions. Appl Math Optim 36:243-262
    • (1997) Appl Math Optim , vol.36 , pp. 243-262
    • Došlá, Z.1    Došlý, O.2
  • 28
    • 0000957621 scopus 로고    scopus 로고
    • Disconjugacy, transformations and quadratic functionals for symplectic dynamic systems on time scales
    • to appear
    • Došlý O, Hilscher R (to appear) Disconjugacy, transformations and quadratic functionals for symplectic dynamic systems on time scales. J Differ Equations Appl
    • J Differ Equations Appl
    • Došlý, O.1    Hilscher, R.2
  • 30
    • 0001341145 scopus 로고
    • Disconjugacy for linear Hamiltonian difference systems
    • Erbe L, Yan P (1992) Disconjugacy for linear Hamiltonian difference systems. J Math Anal Appl 167:355-367
    • (1992) J Math Anal Appl , vol.167 , pp. 355-367
    • Erbe, L.1    Yan, P.2
  • 31
    • 84968495088 scopus 로고
    • Difference equations: Disconjugacy, principal solutions, Green's function, complete monotonicity
    • Hartman P (1978) Difference equations: disconjugacy, principal solutions, Green's function, complete monotonicity. Trans Amer Math Soc 246:1-30
    • (1978) Trans Amer Math Soc , vol.246 , pp. 1-30
    • Hartman, P.1
  • 33
    • 84951604495 scopus 로고
    • Analysis on measure chains - A unified approach to continuous and discrete calculus
    • Hilger S (1990) Analysis on measure chains - a unified approach to continuous and discrete calculus. Results Math 18:18-56
    • (1990) Results Math , vol.18 , pp. 18-56
    • Hilger, S.1
  • 34
    • 0033473928 scopus 로고    scopus 로고
    • Disconjugacy of symplectic systems and positivity of block tridiagonal matrices
    • Hilscher R (1999) Disconjugacy of symplectic systems and positivity of block tridiagonal matrices. Rocky Mountain J Math 29(4):1301-1319
    • (1999) Rocky Mountain J Math , vol.29 , Issue.4 , pp. 1301-1319
    • Hilscher, R.1
  • 35
    • 0033825935 scopus 로고    scopus 로고
    • Linear Hamiltonian systems on time scales: Positivity of quadratic functionals
    • Hilscher R (2000) Linear Hamiltonian systems on time scales: positivity of quadratic functionals. Math Comput Modelling 32(5-6):507-527
    • (2000) Math Comput Modelling , vol.32 , Issue.5-6 , pp. 507-527
    • Hilscher, R.1
  • 36
    • 0000289038 scopus 로고    scopus 로고
    • On disconjugacy for vector linear Hamiltonian systems on time scales
    • (Poznań, 1998), Elaydi S, Ladas G, Popenda J, Rakowski J, editors, Gordon and Breach, Amsterdam
    • Hilscher R (2000) On disconjugacy for vector linear Hamiltonian systems on time scales. In Communications in Difference Equations: Proceedings of the Fourth International Conference on Difference Equations (Poznań, 1998), Elaydi S, Ladas G, Popenda J, Rakowski J, editors, pp 181-188. Gordon and Breach, Amsterdam
    • (2000) Communications in Difference Equations: Proceedings of the Fourth International Conference on Difference Equations , pp. 181-188
    • Hilscher, R.1
  • 37
    • 0035863991 scopus 로고    scopus 로고
    • Inhomogeneous quadratic functionals on time scales
    • Hilscher R (2001) Inhomogeneous quadratic functionals on time scales. J Math Anal Appl 253(2):473-481
    • (2001) J Math Anal Appl , vol.253 , Issue.2 , pp. 473-481
    • Hilscher, R.1
  • 38
    • 85046909456 scopus 로고    scopus 로고
    • Positivity of quadratic functionals on time scales: Necessity
    • to appear
    • Hilscher R (to appear) Positivity of quadratic functionals on time scales: necessity. Math Nachr
    • Math Nachr
    • Hilscher, R.1
  • 39
    • 0001434067 scopus 로고    scopus 로고
    • Discrete optimal control: The accessory problem and necessary optimality conditions
    • Hilscher R, Zeidan V (2000) Discrete optimal control: the accessory problem and necessary optimality conditions. J Math Anal Appl 243(2):429-452
    • (2000) J Math Anal Appl , vol.243 , Issue.2 , pp. 429-452
    • Hilscher, R.1    Zeidan, V.2
  • 43
    • 0000910491 scopus 로고    scopus 로고
    • Nonnegativity and positivity of a quadratic functional
    • Zeidan V (1999) Nonnegativity and positivity of a quadratic functional. Dynam Systems Appl 8(3-4):571-588
    • (1999) Dynam Systems Appl , vol.8 , Issue.3-4 , pp. 571-588
    • Zeidan, V.1
  • 44
    • 0024002202 scopus 로고
    • Necessary conditions for optimal control problems: Conjugate points
    • Zeidan V, Zezza P (1988) Necessary conditions for optimal control problems: conjugate points. SIAM J Control Optim 26(3):592-608
    • (1988) SIAM J Control Optim , vol.26 , Issue.3 , pp. 592-608
    • Zeidan, V.1    Zezza, P.2
  • 45
    • 38249029412 scopus 로고
    • The conjugate point condition for smooth control sets
    • Zeidan V, Zezza P (1988) The conjugate point condition for smooth control sets. J Math Anal Appl 132(2):572-589
    • (1988) J Math Anal Appl , vol.132 , Issue.2 , pp. 572-589
    • Zeidan, V.1    Zezza, P.2
  • 46
    • 0026257766 scopus 로고
    • Coupled points in optimal control theory
    • Zeidan V, Zezza P (1991) Coupled points in optimal control theory. IEEE Trans Automat Control 36(11):1276-1281
    • (1991) IEEE Trans Automat Control , vol.36 , Issue.11 , pp. 1276-1281
    • Zeidan, V.1    Zezza, P.2


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