Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
differential equation; oscillation; second order; delay; neutral type; integral averaging method
differential equation; oscillation; second order; delay; neutral type; integral averaging method
Summary:
We establish some new oscillation criteria for the second order neutral delay differential equation $$ [r(t)|[x(t)+p(t)x[\tau (t)]]'|^{\alpha -1} [x(t)+ p(t)x[\tau (t)]]']' +\,q(t)f(x[\sigma (t)])=0. $$ The obtained results supplement those of Dzurina and Stavroulakis, Sun and Meng, Xu and Meng, Baculíková and Lacková. We also make a slight improvement of one assumption in the paper of Xu and Meng.
References:
[1] Agarwal, R. P., Shieh, S. L., Yeh, C. C.: Oscillation criteria for second-order retarded differential equations. Math. Comput. Modelling 26 (1997), 1-11. DOI 10.1016/S0895-7177(97)00141-6 | MR 1480601 | Zbl 0902.34061
[2] Baculíková, B., Lacková, D.: Oscillation criteria for second order retarded differential equations. Proc. of CDDEA 2006, Studies of the University of \v Zilina 20 (2006), 11-18. MR 2380247
[3] Chern, J. L., Lian, W. Ch., Yeh, C. C.: Oscillation criteria for second order half-linear differential equations with functional arguments. Publ. Math. Debrecen 48 (1996), 209-216. MR 1394842
[4] Džurina, J., Stavroulakis, I. P.: Oscillation criteria for second-order delay differential equations. Appl. Math. Comput. 140 (2003), 445-453. DOI 10.1016/S0096-3003(02)00243-6 | MR 1953915 | Zbl 1043.34071
[5] Elbert, A.: A half-linear second order differential equation. Colloq. Math. Soc. Bolyai 30: Qualitative Theory of Differential Equations (Szeged) (1979), 153-180. MR 0680591
[6] Elbert, A.: Oscillation and nonoscillation theorems for some nonlinear ordinary differential equations. Lecture Notes in Math., Ordinary and Partial Differential Equations 964 (1982), 187-212. DOI 10.1007/BFb0064999 | MR 0693113 | Zbl 0528.34034
[7] Hardy, G. H., Littlewood, J. E., Polya, G.: Inequalities. Second ed., Cambridge University Press, Cambridge (1952). MR 0046395 | Zbl 0047.05302
[8] Kusano, T., Naito, Y., Ogata, A.: Strong oscillation and nonoscillation of quasilinear differential equations of second order. Differ. Equ. Dyn. Syst. 2 (1994), 1-10. MR 1386034
[9] Kusano, T., Yoshida, N.: Nonoscillation theorems for a class of quasilinear differential equations of second order. J. Math. Anal. Appl. 189 (1995), 115-127. DOI 10.1006/jmaa.1995.1007 | MR 1312033
[10] Li, W. T.: Interval oscillation of the second-order half-linear functional differential equations. Appl. Math. Comput. 155 (2004), 451-468. DOI 10.1016/S0096-3003(03)00790-2 | MR 2077061
[11] Mirzov, D. D.: On the oscillation of a system of nonlinear differential equations. Diferencialnye Uravnenija 9 (1973), 581-583 Russian. MR 0315209
[12] Mirzov, D. D.: On some analogs of Sturm's and Kneser's theorems for nonlinear systems. J. Math. Anal. Appl. 53 (1976), 418-425. DOI 10.1016/0022-247X(76)90120-7 | MR 0402184 | Zbl 0327.34027
[13] Mirzov, D. D.: On the oscillation of solutions of a system of differential equations. Mat. Zametki 23 (1978), 401-404 Russian. MR 0492540
[14] Sun, Y. G., Meng, F. W.: Note on the paper of Džurina and Stavroulakis. Appl. Math. Comput. 174 (2006), 1634-1641. DOI 10.1016/j.amc.2005.07.008 | MR 2220639 | Zbl 1096.34048
[15] Xu, R., Meng, F. W.: Some new oscillation criteria for second order quasi-linear neutral delay differential equations. Appl. Math. Comput. 182 (2006), 797-803. DOI 10.1016/j.amc.2006.04.042 | MR 2292088 | Zbl 1115.34341
Search
Partner of
