| Title:
|
Oscillation of certain difference equations (English) |
| Author:
|
Grace, S. R. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
50 |
| Issue:
|
2 |
| Year:
|
2000 |
| Pages:
|
347-358 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Some new criteria for the oscillation of difference equations of the form \[ \Delta ^2 x_n - p_n \Delta x_{n-h} + q_n |x_{g_n}|^c \mathop {\mathrm sgn}x_{g_n} = 0 \] and \[ \Delta ^i x_n + p_n \Delta ^{i-1} x_{n-h} + q_n |x_{g_n}|^c \mathop {\mathrm sgn}x_{g_n} = 0, \ i = 2,3, \] are established. (English) |
| MSC:
|
39A10 |
| MSC:
|
39A11 |
| idZBL:
|
Zbl 1051.39005 |
| idMR:
|
MR1761392 |
| . |
| Date available:
|
2009-09-24T10:33:19Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127574 |
| . |
| Reference:
|
[1] S. R. Grace: On the oscillatory and asymptotic behavior of damped functional differential equations.Math. Japon. 36 (1991), 229–237. Zbl 0732.34056, MR 1095734 |
| Reference:
|
[2] S. R. Grace: Oscillatory and asymptotic behavior of damped functional differential equations.Math. Nachr. 142 (1989), 279–305. Zbl 0698.34060, MR 1017387 |
| Reference:
|
[3] S. R. Grace: Oscillation theorems for damped functional differential equations.Funkcial. Ekvac. 35 (1992), 261–278. Zbl 0758.34053, MR 1189896 |
| Reference:
|
[4] S. R. Grace, B. S. Lalli: Oscillation theorems for second order delay and neutral difference equations.Utilitas Math. 45 (1994), 197–211. MR 1284030 |
| Reference:
|
[5] S. R. Grace, B. S. Lalli: Oscillation theorems for forced neutral difference equations.J. Math. Anal. Appl. 187 (1994), 91–106. MR 1296607, 10.1006/jmaa.1994.1346 |
| Reference:
|
[6] I. Györi, G. Ladas: Oscillation Theory of Delay Differential Equations with Applications.Oxford University Press, Oxford, 1991. MR 1168471 |
| Reference:
|
[7] J. W. Hooker, W. T. Patula: A second order nonlinear difference equation: Oscillation and asymptotic behavior.J. Math. Anal. Appl. 91 (1983), 9–29. MR 0688528, 10.1016/0022-247X(83)90088-4 |
| Reference:
|
[8] G. Ladas, C. Qian: Comparison results and linearized oscillations for higher order difference equations.Internat. J. Math. & Math. Sci. 15 (1992), 129–142. MR 1143937, 10.1155/S0161171292000152 |
| Reference:
|
[9] B. S. Lalli, S. R. Grace: Oscillation theorems for second order neutral difference equations.Appl. Math. Comput. 62 (1994), 47–60. MR 1274100, 10.1016/0096-3003(94)90132-5 |
| Reference:
|
[10] W. T. Patula: Growth and oscillation properties of second order linear difference equations.SIAM J. Math. Anal. 10 (1979), 55–61. Zbl 0397.39001, MR 0516749, 10.1137/0510006 |
| Reference:
|
[11] Ch. G. Philos: On oscillation of some difference equations.Funkcial. Ekvac. 34 (1991), 157–172. MR 1116887 |
| Reference:
|
[12] F. Weil: Existence theorem for the difference equation $y_{n+1} - 2y_n + y_{n-1} = h^2 f(y_n)$.Internat. J. Math. & Math. Sci. 3 (1990), 69–77. MR 0576630 |
| . |
