Oscillatory and nonoscillatory behaviour of solutions of difference equations of the third order

N. Parhi; Anita Panda

Mathematica Bohemica (2008)

  • Volume: 133, Issue: 1, page 99-112
  • ISSN: 0862-7959

Abstract

top
In this paper, sufficient conditions are obtained for oscillation of all solutions of third order difference equations of the form y n + 3 + r n y n + 2 + q n y n + 1 + p n y n = 0 , n ≥ 0 . These results are generalization of the results concerning difference equations with constant coefficients y n + 3 + r y n + 2 + q y n + 1 + p y n = 0 , n ≥ 0 . Oscillation, nonoscillation and disconjugacy of a certain class of linear third order difference equations are discussed with help of a class of linear second order difference equations.

How to cite

top

Parhi, N., and Panda, Anita. "Oscillatory and nonoscillatory behaviour of solutions of difference equations of the third order." Mathematica Bohemica 133.1 (2008): 99-112. <http://eudml.org/doc/32574>.

@article{Parhi2008,
abstract = {In this paper, sufficient conditions are obtained for oscillation of all solutions of third order difference equations of the form \[ y\_\{n+3\} +r\_\{n\} y\_\{n+2\} +q\_\{n\} y\_\{n+1\} +p\_\{n\} y\_\{n\} =0,\quad n\ge 0. \] These results are generalization of the results concerning difference equations with constant coefficients \[y\_\{n+3\} +ry\_\{n+2\} +qy\_\{n+1\} +py\_\{n\} =0,\quad n\ge 0.\] Oscillation, nonoscillation and disconjugacy of a certain class of linear third order difference equations are discussed with help of a class of linear second order difference equations.},
author = {Parhi, N., Panda, Anita},
journal = {Mathematica Bohemica},
keywords = {third order difference equation; oscillation; nonoscillation; disconjugacy; generalized zero; third order difference equation; oscillation; nonoscillation; disconjugacy; generalized zero},
language = {eng},
number = {1},
pages = {99-112},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillatory and nonoscillatory behaviour of solutions of difference equations of the third order},
url = {http://eudml.org/doc/32574},
volume = {133},
year = {2008},
}

TY - JOUR
AU - Parhi, N.
AU - Panda, Anita
TI - Oscillatory and nonoscillatory behaviour of solutions of difference equations of the third order
JO - Mathematica Bohemica
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 133
IS - 1
SP - 99
EP - 112
AB - In this paper, sufficient conditions are obtained for oscillation of all solutions of third order difference equations of the form \[ y_{n+3} +r_{n} y_{n+2} +q_{n} y_{n+1} +p_{n} y_{n} =0,\quad n\ge 0. \] These results are generalization of the results concerning difference equations with constant coefficients \[y_{n+3} +ry_{n+2} +qy_{n+1} +py_{n} =0,\quad n\ge 0.\] Oscillation, nonoscillation and disconjugacy of a certain class of linear third order difference equations are discussed with help of a class of linear second order difference equations.
LA - eng
KW - third order difference equation; oscillation; nonoscillation; disconjugacy; generalized zero; third order difference equation; oscillation; nonoscillation; disconjugacy; generalized zero
UR - http://eudml.org/doc/32574
ER -

References

top
  1. 10.1016/0898-1221(94)00101-4, Comput. Math. Appl. 28 (1994), 131–139. (1994) MR1284228DOI10.1016/0898-1221(94)00101-4
  2. 10.1016/0022-247X(81)90208-0, J. Math. Anal. Appl. 82 (1981), 451–462. (1981) MR0629769DOI10.1016/0022-247X(81)90208-0
  3. Difference Equations: An Introduction with Applications, Academic Press, New York, 1991. (1991) MR1142573
  4. 10.1080/10236190008808213, J. Difference Eqns. Appl. 6 (2000), 53–74. (2000) MR1752155DOI10.1080/10236190008808213
  5. 10.1080/10236190290017423, J. Difference Eqns. Appl. 8 (2002), 415–426. (2002) MR1897066DOI10.1080/10236190290017423
  6. Study of Oscillatory and Asymptotic Behaviour of Solutions of Difference Equations, Ph.D. thesis. 

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.