| Title:
|
Oscillatory and nonoscillatory behaviour of solutions of difference equations of the third order (English) |
| Author:
|
Parhi, N. |
| Author:
|
Panda, Anita |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
133 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
99-112 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
third order difference equation |
| Keyword:
|
oscillation |
| Keyword:
|
nonoscillation |
| Keyword:
|
disconjugacy |
| Keyword:
|
generalized zero |
| MSC:
|
39A06 |
| MSC:
|
39A10 |
| MSC:
|
39A11 |
| MSC:
|
39A12 |
| MSC:
|
39A21 |
| idZBL:
|
Zbl 1199.39016 |
| idMR:
|
MR2400154 |
| DOI:
|
10.21136/MB.2008.133942 |
| . |
| Date available:
|
2009-09-24T22:34:57Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133942 |
| . |
| Reference:
|
[1] J. Henderson, A. Peterson: Disconjugacy for a third order linear difference equation.Comput. Math. Appl. 28 (1994), 131–139. MR 1284228, 10.1016/0898-1221(94)00101-4 |
| Reference:
|
[2] J. W. Hooker, W. T. Patula: Riccati type transformations for second order linear difference equations.J. Math. Anal. Appl. 82 (1981), 451–462. MR 0629769, 10.1016/0022-247X(81)90208-0 |
| Reference:
|
[3] W. G. Kelley, A. C. Peterson: Difference Equations: An Introduction with Applications.Academic Press, New York, 1991. MR 1142573 |
| Reference:
|
[4] N. Parhi, A. K. Tripathy: On oscillatory third order difference equations.J. Difference Eqns. Appl. 6 (2000), 53–74. MR 1752155, 10.1080/10236190008808213 |
| Reference:
|
[5] N. Parhi, A. K. Tripathy: On the behaviour of solutions of a class of third order difference equations.J. Difference Eqns. Appl. 8 (2002), 415–426. MR 1897066, 10.1080/10236190290017423 |
| Reference:
|
[6] A. K. Tripathy: Study of Oscillatory and Asymptotic Behaviour of Solutions of Difference Equations.Ph.D. thesis. |
| . |
