| Title:
|
Oscillatory properties of solutions of second order nonlinear neutral differential inequalities with oscillating coefficients (English) |
| Author:
|
Grammatikopoulos, M. K. |
| Author:
|
Marušiak, P. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
31 |
| Issue:
|
1 |
| Year:
|
1995 |
| Pages:
|
29-36 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper deals with the second order nonlinear neutral differential inequalities $(A_\nu )$: $(-1)^\nu x(t)\,\lbrace \,z^{\prime \prime }(t)+(-1)^\nu q(t)\,f(x(h(t))) \rbrace \le 0,\ $ $t\ge t_0\ge 0,$ where $\ \nu =0\ $ or $\ \nu =1,\ $ $\ z(t)\,=\,x(t)\,+\,p(t)\,x(t-\tau ),\ $ $\ 0<\tau =\ $ const, $\ p,q,h:[t_0,\infty )\rightarrow R\ $ $\ f:R\rightarrow R\ $ are continuous functions. There are proved sufficient conditions under which every bounded solution of $(A_\nu )$ is either oscillatory or $\ \liminf \limits _{t\rightarrow \infty }|x(t)|=0.$ (English) |
| Keyword:
|
neutral differential equations |
| Keyword:
|
oscillatory (nonoscillatory) solutions |
| MSC:
|
34A40 |
| MSC:
|
34C10 |
| MSC:
|
34K11 |
| MSC:
|
34K15 |
| MSC:
|
34K25 |
| MSC:
|
34K40 |
| idZBL:
|
Zbl 0832.34066 |
| idMR:
|
MR1342372 |
| . |
| Date available:
|
2008-06-06T21:27:42Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107521 |
| . |
| Reference:
|
[1] Bainov, D. D., Mishev, D. P.: Oscillation Theory for Neutral Equations with Delay.Adam Hilger IOP Pablisching Ltd. (1991) 288pp.. |
| Reference:
|
[2] Grammatikopoulos, M. K., Grove, E. A., Ladas, G.: Oscillation and asymptotic behavior of second order neutral differential equations with deviating arguments.Canad. Math. Soc. V8 (1967) 153$-$161. MR 0909906 |
| Reference:
|
[3] Graef, J. R., Grammatikopoulos, M. K., Spikes, P. W.: Asymptotic Properties of Solutions of Neutral Delay Differential Equations of the Second Order.Radovi Matematički $\ V_4\ $ (1988) 113 $-$149. |
| Reference:
|
[4] Graef, J. R., Grammatikopoulos, M. K., Spikes, P. W.: On the Asymptitic Behavior of Solutions of Second Order Nonlinear Neutral Delay Differential Equations,.Journal Math. Anal. Appl. V156 $N_1$ (1991) 23$-$39. MR 1102594 |
| Reference:
|
[5] Graef, J. R., Grammatikopoulos, M. K., Spikes, P. W.: Asymptotic Behavior of Nonoscillatory Solutions of Neutral Delay Differential Equations of Arbitrary Order.Nonlinear Analysis, Theory, Math., Appl. V21, N1 (1993) 23$-$42. MR 1231526 |
| Reference:
|
[6] Györi, I., Ladas, G.: Oscillation Theory of Delay Differential Equations.Clear. Press., Oxford (1991) 368pp. MR 1168471 |
| Reference:
|
[7] Jaroš, J., Kussano, T.: Sufficient conditions for oscillations of higher order linear functional differential equations of neutral type.Japan J. Math.15 (1989) 415$-$432. MR 1039249 |
| Reference:
|
[8] Jaroš, J., Kusano, T.: Oscillation properties of first order nonlinear functional differential equations of neutral type.Diff. and Int. Equat. (1991) 425$-$436. MR 1081192 |
| Reference:
|
[9] Kusano, T., Onose, H.: Nonoscillation theorems for differential equation with deviating argument.Pacific J. Math. 63, $N_1$ (1976) 185$-$192. MR 0417536 |
| . |
