| Title:
|
Some oscillation criteria for the second-order linear delay differential equation (English) |
| Author:
|
Opluštil, Zdeněk |
| Author:
|
Šremr, Jiří |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
136 |
| Issue:
|
2 |
| Year:
|
2011 |
| Pages:
|
195-204 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Some Wintner and Nehari type oscillation criteria are established for the second-order linear delay differential equation. (English) |
| Keyword:
|
second-order linear differential equation with a delay |
| Keyword:
|
oscillatory solution |
| MSC:
|
34K06 |
| MSC:
|
34K11 |
| idZBL:
|
Zbl 1224.34215 |
| idMR:
|
MR2856136 |
| DOI:
|
10.21136/MB.2011.141582 |
| . |
| Date available:
|
2011-06-07T11:31:18Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141582 |
| . |
| Reference:
|
[1] Fite, W. B.: Concerning the zeros of the solutions of certain differential equations.Trans. Amer. Math. Soc. 19 (1918), 341-352 \JFM 46.0702.02. MR 1501107, 10.1090/S0002-9947-1918-1501107-2 |
| Reference:
|
[2] Došlý, O., Řehák, P.: Half-linear Differential Equations.North-Holland Mathematics Studies 202, Elsevier, Amsterdam (2005). Zbl 1090.34001, MR 2158903 |
| Reference:
|
[3] Hartman, P.: Ordinary Differential Equations.John Wiley, New York (1964). Zbl 0125.32102, MR 0171038 |
| Reference:
|
[4] Hille, E.: Non-oscillation theorems.Trans. Amer. Math. Soc. 64 (1948), 234-252. Zbl 0031.35402, MR 0027925, 10.1090/S0002-9947-1948-0027925-7 |
| Reference:
|
[5] Kandelaki, N., Lomtatidze, A., Ugulava, D.: On oscillation and nonoscillation of a second order half-linear equation.Georgian Math. J. 7 (2000), 329-346. MR 1779555, 10.1515/GMJ.2000.329 |
| Reference:
|
[6] Koplatadze, R.: On oscillatory solutions of second order delay differential inequalities.J. Math. Anal. Appl. 42 (1973), 148-157. Zbl 0255.34069, MR 0322313, 10.1016/0022-247X(73)90127-3 |
| Reference:
|
[7] Koplatadze, R.: Oscillation criteria for solutions of second order differential inequalities and equations with retarded argument.Tr. Inst. Prikl. Mat. Im. I. N. Vekua 17 (1986), 104-121 Russian. Zbl 0645.34027, MR 0853276 |
| Reference:
|
[8] Müller-Pfeiffer, E.: Oscillation criteria of Nehari-type for Schrödinger equation.Math. Nachr. 96 (1980), 185-194. MR 0600809, 10.1002/mana.19800960116 |
| Reference:
|
[9] Myshkis, A. D.: Linear Differential Equations with Retarded Argument.Nauka, Moskva (1972), Russian. Zbl 0261.34040, MR 0352648 |
| Reference:
|
[10] Nehari, Z.: Oscillation criteria for second-order linear differential equations.Trans. Amer. Math. Soc. 85 (1957), 428-445. Zbl 0078.07602, MR 0087816, 10.1090/S0002-9947-1957-0087816-8 |
| Reference:
|
[11] Opluštil, Z., Pospíšil, Z.: An oscillation criterion for a dynamic Sturm-Liouville equation, New progress in difference equations.Proceedings of the 6th International Conference on Difference Equations (2004), 317-324. MR 2092567 |
| Reference:
|
[12] Partsvania, N.: On oscillation of solutions of second-order systems of deviated differential equations.Georgian Math. J. 3 (1996), 571-582. Zbl 0868.34054, MR 1419836, 10.1007/BF02259985 |
| Reference:
|
[13] Partsvania, N.: On oscillatory and monote solutions of two-dimensional differential systems with deviated arguments.Ph.D. Thesis, A. Razmadze Mathematical Institute of the Georgian Academy of Sciences, Tbilisi (1999). |
| Reference:
|
[14] Partsvania, N.: On the oscillation of solutions od two-dimensional linear differential systems with deviated arguments.Mem. Differential Equations Math. Phys. 13 (1998), 148-149. MR 1632394 |
| Reference:
|
[15] Řehák, P.: Half-linear dynamic equations on time scales: IVP and oscillatory properties.Nonlinear Funct. Anal. Appl. 7 (2002), 361-403. Zbl 1037.34002, MR 1946469 |
| Reference:
|
[16] Řehák, P.: Hartman-Wintner type lemma, oscillation, and conjugacy criteria for half-linear difference equations.J. Math. Anal. Appl. 252 (2000), 813-827. MR 1800179, 10.1006/jmaa.2000.7124 |
| Reference:
|
[17] Swanson, C. A.: Comparison and Oscillation Theory of Linear Differential Equations.Academic Press, New York (1968). Zbl 0191.09904, MR 0463570 |
| Reference:
|
[18] Willett, D.: Classification of second order linear differential equations with respect to oscillation.Adv. Math. 3 (1969), 594-623. Zbl 0188.40101, MR 0280800, 10.1016/0001-8708(69)90011-5 |
| Reference:
|
[19] Wintner, A.: On the non-existence of conjugate points.Amer. J. Math. 73 (1951), 368-380. MR 0042005, 10.2307/2372182 |
| . |
