Conjugacy criteria for second order linear difference equations

Ondřej Došlý; Pavel Řehák

Archivum Mathematicum (1998)

  • Volume: 034, Issue: 2, page 301-310
  • ISSN: 0044-8753

Abstract

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We establish conditions which guarantee that the second order difference equation Δ 2 x k + p k x k + 1 = 0 possesses a nontrivial solution with at least two generalized zero points in a given discrete interval

How to cite

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Došlý, Ondřej, and Řehák, Pavel. "Conjugacy criteria for second order linear difference equations." Archivum Mathematicum 034.2 (1998): 301-310. <http://eudml.org/doc/248197>.

@article{Došlý1998,
abstract = {We establish conditions which guarantee that the second order difference equation \[\Delta ^2x\_k+p\_k x\_\{k+1\}=0\] possesses a nontrivial solution with at least two generalized zero points in a given discrete interval},
author = {Došlý, Ondřej, Řehák, Pavel},
journal = {Archivum Mathematicum},
keywords = {Discrete conjugacy criteria; discrete Riccati equation; phase function; generalized zero points; discrete conjugacy criteria; discrete Riccati equation; phase function; generalized zero points; oscillatory properties; second order difference equation},
language = {eng},
number = {2},
pages = {301-310},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Conjugacy criteria for second order linear difference equations},
url = {http://eudml.org/doc/248197},
volume = {034},
year = {1998},
}

TY - JOUR
AU - Došlý, Ondřej
AU - Řehák, Pavel
TI - Conjugacy criteria for second order linear difference equations
JO - Archivum Mathematicum
PY - 1998
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 034
IS - 2
SP - 301
EP - 310
AB - We establish conditions which guarantee that the second order difference equation \[\Delta ^2x_k+p_k x_{k+1}=0\] possesses a nontrivial solution with at least two generalized zero points in a given discrete interval
LA - eng
KW - Discrete conjugacy criteria; discrete Riccati equation; phase function; generalized zero points; discrete conjugacy criteria; discrete Riccati equation; phase function; generalized zero points; oscillatory properties; second order difference equation
UR - http://eudml.org/doc/248197
ER -

References

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  13. Nodal domains of one– or two–dimensional elliptic differential equations, Z. Anal. Anwendungen 7 (1988), 135-139. (1988) MR0951346
  14. Generalized linear differential systems, J. Math. Mech. 8 (1959), 705-726. (1959) Zbl0094.06001MR0107050
  15. [unknown], Comparison and Oscillation Theory of Linear Differential Equations, Acad. Press, New York, 1968. Zbl1168.92026MR0463570
  16. Mémoire sur le équations differentielles linéaries du second ordre, Journal de Mathématiques Pures et Appliquées 1 (1836), 106-186. (1836) 
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  18. Classification of second order linear differential equations with respect to oscillation, Advances in Mathematics 3 (1969), 594-623. (1969) MR0280800

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