Keywords: second-order linear differential equation with a delay; oscillatory solution
@article{10_21136_MB_2011_141582,
author = {Oplu\v{s}til, Zden\v{e}k and \v{S}remr, Ji\v{r}{\'\i}},
title = {Some oscillation criteria for the second-order linear delay differential equation},
journal = {Mathematica Bohemica},
pages = {195--204},
year = {2011},
volume = {136},
number = {2},
doi = {10.21136/MB.2011.141582},
mrnumber = {2856136},
zbl = {1224.34215},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2011.141582/}
}
TY - JOUR AU - Opluštil, Zdeněk AU - Šremr, Jiří TI - Some oscillation criteria for the second-order linear delay differential equation JO - Mathematica Bohemica PY - 2011 SP - 195 EP - 204 VL - 136 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.21136/MB.2011.141582/ DO - 10.21136/MB.2011.141582 LA - en ID - 10_21136_MB_2011_141582 ER -
%0 Journal Article %A Opluštil, Zdeněk %A Šremr, Jiří %T Some oscillation criteria for the second-order linear delay differential equation %J Mathematica Bohemica %D 2011 %P 195-204 %V 136 %N 2 %U http://geodesic.mathdoc.fr/articles/10.21136/MB.2011.141582/ %R 10.21136/MB.2011.141582 %G en %F 10_21136_MB_2011_141582
Opluštil, Zdeněk; Šremr, Jiří. Some oscillation criteria for the second-order linear delay differential equation. Mathematica Bohemica, Tome 136 (2011) no. 2, pp. 195-204. doi: 10.21136/MB.2011.141582
[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. | DOI | MR
[2] Došlý, O., Řehák, P.: Half-linear Differential Equations. North-Holland Mathematics Studies 202, Elsevier, Amsterdam (2005). | MR | Zbl
[3] Hartman, P.: Ordinary Differential Equations. John Wiley, New York (1964). | MR | Zbl
[4] Hille, E.: Non-oscillation theorems. Trans. Amer. Math. Soc. 64 (1948), 234-252. | DOI | MR | Zbl
[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. | DOI | MR
[6] Koplatadze, R.: On oscillatory solutions of second order delay differential inequalities. J. Math. Anal. Appl. 42 (1973), 148-157. | DOI | MR | Zbl
[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. | MR | Zbl
[8] Müller-Pfeiffer, E.: Oscillation criteria of Nehari-type for Schrödinger equation. Math. Nachr. 96 (1980), 185-194. | DOI | MR
[9] Myshkis, A. D.: Linear Differential Equations with Retarded Argument. Nauka, Moskva (1972), Russian. | MR | Zbl
[10] Nehari, Z.: Oscillation criteria for second-order linear differential equations. Trans. Amer. Math. Soc. 85 (1957), 428-445. | DOI | MR | Zbl
[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
[12] Partsvania, N.: On oscillation of solutions of second-order systems of deviated differential equations. Georgian Math. J. 3 (1996), 571-582. | DOI | MR | Zbl
[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).
[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
[15] Řehák, P.: Half-linear dynamic equations on time scales: IVP and oscillatory properties. Nonlinear Funct. Anal. Appl. 7 (2002), 361-403. | MR | Zbl
[16] Řehák, P.: Hartman-Wintner type lemma, oscillation, and conjugacy criteria for half-linear difference equations. J. Math. Anal. Appl. 252 (2000), 813-827. | DOI | MR
[17] Swanson, C. A.: Comparison and Oscillation Theory of Linear Differential Equations. Academic Press, New York (1968). | MR | Zbl
[18] Willett, D.: Classification of second order linear differential equations with respect to oscillation. Adv. Math. 3 (1969), 594-623. | DOI | MR | Zbl
[19] Wintner, A.: On the non-existence of conjugate points. Amer. J. Math. 73 (1951), 368-380. | DOI | MR
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