Oscillation Theory of Linear Difference Equations

Ondřej Došlý

Archivum Mathematicum (2000)

  • Volume: 036, Issue: 5, page 329-342
  • ISSN: 0044-8753

How to cite

top

Došlý, Ondřej. "Oscillation Theory of Linear Difference Equations." Archivum Mathematicum 036.5 (2000): 329-342. <http://eudml.org/doc/248574>.

@article{Došlý2000,
author = {Došlý, Ondřej},
journal = {Archivum Mathematicum},
keywords = {discrete oscillation theory; Sturm-Liouville difference equation; Riccati equation; variational principle; symplectic system},
language = {eng},
number = {5},
pages = {329-342},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Oscillation Theory of Linear Difference Equations},
url = {http://eudml.org/doc/248574},
volume = {036},
year = {2000},
}

TY - JOUR
AU - Došlý, Ondřej
TI - Oscillation Theory of Linear Difference Equations
JO - Archivum Mathematicum
PY - 2000
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 036
IS - 5
SP - 329
EP - 342
LA - eng
KW - discrete oscillation theory; Sturm-Liouville difference equation; Riccati equation; variational principle; symplectic system
UR - http://eudml.org/doc/248574
ER -

References

top
  1. 1. R. P. Agarwal, Difference Equations and Inequalities: Theory, Methods and Applications, Second Edition, Pure and Applied Mathematics, M. Dekker, New York - Basel - Hong Kong, 2000. Zbl0952.39001MR1740241
  2. 2. C. D. Ahlbrandt A. C. Peterson, Discrete Hamiltonian Systems: Difference Equations, Continued Fractions, and Riccati Equations, Kluwer Academic Publishers, Boston, 1996. (1996) MR1423802
  3. 3. D. Anderson, Discrete trigonometric matrix functions, Panamer. Math. J. 7 (1997), 39-54. (1997) Zbl0888.39010MR1427019
  4. 4. J. H. Barrett, A Prüfer transformation for matrix differential equations, Proc. Amer. Math. Soc. 8 (1957), 510-518. (1957) Zbl0079.10603MR0087821
  5. 5. M. Bohner, Linear Hamiltonian difference systems: disconjugacy and Jacobi-type conditions, J. Math. Anal. Appl. 199 (1996), 804–826. (199) MR1386607
  6. 6. M. Bohner O. Došlý, Disconjugacy and transformations for symplectic systems, Rocky Mountain J. Math. 27 (1997), 707–743. (1997) MR1490271
  7. 7. M. Bohner O. Došlý, Trigonometric transformation of symplectic difference systems, J. Differential Equ. 163 (2000), 113-129. MR1755071
  8. 8. M. Bohner O. Došlý, Discrete Prüfer transformation, to appear in Proc. Amer. Math. Soc. MR1838796
  9. 9. W. A. Coppel, Disconjugacy, Lectures Notes in Math., No. 220, Springer Verlag, Berlin-Heidelberg 1971. (1971) Zbl0224.34003MR0460785
  10. 10. O. Došlý, On transformations of self-adjoint differential systems and their reciprocals, Ann. Polon. Math. 50 (1990), 223-234. (1990) MR1064996
  11. 11. O. Došlý, Oscillation criteria for higher order Sturm-Liouville difference equations, J. Differ. Equations Appl. 4 (1998), 425-450. (1998) MR1665162
  12. 12. O. Došlý, Methods of oscillation theory of half-linear second order differential equations, Czech. Math. J. 50 (125) (2000), 657-671. MR1777486
  13. 13. O. Došlý R. Hilscher, A class of Sturm-Liouville difference equations: (non)oscillation constants and property BD, submitted. 
  14. 14. O. Došlý J. Osička, Kneser-type oscillation criteria for self-adjoint, two term, differential equations, Georgian J. Math., 2 (1995), 241-258. (1995) MR1334880
  15. 15. O. Došlý J. Osička, Oscillation and nonoscillation of higher order self-adjoint differential equations, to appear in Czech. Math. J. MR1940063
  16. 16. O. Došlý P. Řehák, Nonoscillation criteria for half-linear second order difference equations, to appear in Comput. Appl. Math. MR1838006
  17. 17. S. N. Elaydi, An Introduction to Difference Equations, Second Edition, Springer Verlag, 2000. Zbl1071.39001MR1711587
  18. 18. U. Elias, Oscillation Theory of Two-Term Differential equations, Kluwer, Dordrecht-Boston-London, 1997. (1997) Zbl0878.34022MR1445292
  19. 19. I. M. Gelfand S. V. Fomin, Calculus of Variations, Prentice Hall, Engelwood, 1963. (1963) MR0160139
  20. 20. B. Harris R. J. Kruger W. T.Trench, Trench’s canonical form for a disconjugate n-th order linear difference equations, Panamer. Math. J. 8 (1998), 55-71. (1998) MR1642648
  21. 21. P. Hartman, Difference equations: disconjugacy, principal solutions, Green’s function, complete monotonicity, Trans. Amer. Math. Soc. 246 (1978), 1–30. (1978) MR0515528
  22. 22. W. G. Kelley A. Peterson, Difference Equations: An Introduction with Applications, Acad. Press, San Diego, 1991. (1991) MR1142573
  23. 23. S. Peňa, Discrete spectra criteria for singular difference operators, Math. Bohem. 124 (1999), 35–44. (1999) MR1687425
  24. 24. G. Polya, On the mean-value theorem corresponding to a given linear homogeneous differential equation, Trans. Amer. Math. Soc. 24 (1924), 312-324. (1924) MR1501228
  25. 25. H. Prüfer, Neue Herleitung der Sturm-Liouvilleschen Reihenentwicklung stetiger Funktionen, Math. Ann. 95 (1926), 499-518. (1926) MR1512291
  26. 26. W. T. Reid, Sturmian Theory for Ordinary Differential Equations, Springer Verlag, New York-Heidelberg-Berlin 1980. (1980) Zbl0459.34001MR0606199
  27. 27. W. F. Trench, Canonical forms and principal systems of general disconjugate equations, Trans. Amer. Math. Soc. 189 (1974), 319-327. (1974) MR0330632

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.