Applications of time scale symplectic systems without normality

Journal of Mathematical Analysis and Applications

Volumn 340, Issue 1, 2008, Pages 451-465

  Hilscher, Roman ^a   Zeidan, Vera ^b  

^a MASARYK UNIVERSITY   (Czech Republic)

^b MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

Conjoined basis; Linear Hamiltonian system; Nonnegativity; Positivity; Quadratic functional; Riccati matrix equation; Time scale; Time scale symplectic system

Indexed keywords

EID: 37449024882     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.07.077     Document Type: Article

References (22)

1. Allwright J., and Vinter R. Second order conditions for periodic optimal control problems. Control Cybernet. 34 3 (2005) 617-643
2. Bohner M. Linear Hamiltonian difference systems: Disconjugacy and Jacobi-type conditions. J. Math. Anal. Appl. 199 3 (1996) 804-826
3. Bohner M. Discrete Sturmian theory. Ulmer Seminare, vol. 1. University of Ulm, 1996. Math. Inequal. Appl. 1 3 (1998) 375-383
4. Bohner M., and Došlý O. Disconjugacy and transformations for symplectic systems. Rocky Mountain J. Math. 27 3 (1997) 707-743
5. Bohner M., Došlý O., and Kratz W. A Sturmian theorem for recessive solutions of linear Hamiltonian difference systems. Appl. Math. Lett. 12 (1999) 101-106
6. Bohner M., Došlý O., and Kratz W. Discrete Reid roundabout theorems. In: Agarwal R.P., and Bohner M. (Eds). Discrete and Continuous Hamiltonian Systems. Dynam. Systems Appl. 8 3-4 (1999) 345-352
7. Bohner M., and Peterson A. Dynamic Equations on Time Scales. An Introduction with Applications (2001), Birkhäuser, Boston
8. Bohner M., and Peterson A. Advances in Dynamic Equations on Time Scales (2003), Birkhäuser, Boston
9. Došlý O., Hilger S., and Hilscher R. Symplectic dynamic systems. In: Bohner M., and Peterson A. (Eds). Advances in Dynamic Equations on Time Scales (2003), Birkhäuser, Boston 293-334
10. Došlý O., and Hilscher R. Disconjugacy, transformations and quadratic functionals for symplectic dynamic systems on time scales. J. Difference Equ. Appl. 7 (2001) 265-295
11. Došlý O., and Kratz W. A Sturmian separation theorem for symplectic difference systems. J. Math. Anal. Appl. 325 1 (2007) 333-341
12. Hilger S. Analysis on measure chains-A unified approach to continuous and discrete calculus. Results Math. 18 1-2 (1990) 18-56
13. Hilscher R. Reid roundabout theorem for symplectic dynamic systems on time scales. Appl. Math. Optim. 43 2 (2001) 129-146
14. Hilscher R., and Růžičková V. Riccati inequality and other results for discrete symplectic systems. J. Math. Anal. Appl. 322 2 (2006) 1083-1098
15. Hilscher R., and Řehák P. Riccati inequality, disconjugacy, and reciprocity principle for linear Hamiltonian dynamic systems. In: Bohner M., and Kaymakçalan B. (Eds). Dynamic Equations on Time Scales. Dynam. Systems Appl. 12 1-2 (2003) 171-189
16. Hilscher R., and Zeidan V. Symplectic difference systems: Variable stepsize discretization and discrete quadratic functionals. Linear Algebra Appl. 367 (2003) 67-104
17. Hilscher R., and Zeidan V. Time scale symplectic systems without normality. J. Differential Equations 230 1 (2006) 140-173
18. Kratz W. Quadratic Functionals in Variational Analysis and Control Theory (1995), Akademie-Verlag, Berlin
19. Kratz W. Discrete oscillation. J. Difference Equ. Appl. 9 1 (2003) 135-147
20. Kratz W. Definiteness of quadratic functionals. Analysis (Munich) 23 2 (2003) 163-183
21. Reid W.T. Ordinary Differential Equations (1971), Wiley, New York
22. Reid W.T. Riccati Differential Equations (1972), Academic Press, New York