Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
second-order linear differential equation with a delay; oscillatory solution
second-order linear differential equation with a delay; oscillatory solution
Summary:
Some Wintner and Nehari type oscillation criteria are established for the second-order linear delay differential equation.
References:
[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 10.1090/S0002-9947-1918-1501107-2 | MR 1501107
[2] Došlý, O., Řehák, P.: Half-linear Differential Equations. North-Holland Mathematics Studies 202, Elsevier, Amsterdam (2005). MR 2158903 | Zbl 1090.34001
[3] Hartman, P.: Ordinary Differential Equations. John Wiley, New York (1964). MR 0171038 | Zbl 0125.32102
[4] Hille, E.: Non-oscillation theorems. Trans. Amer. Math. Soc. 64 (1948), 234-252. DOI 10.1090/S0002-9947-1948-0027925-7 | MR 0027925 | Zbl 0031.35402
[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 10.1515/GMJ.2000.329 | MR 1779555
[6] Koplatadze, R.: On oscillatory solutions of second order delay differential inequalities. J. Math. Anal. Appl. 42 (1973), 148-157. DOI 10.1016/0022-247X(73)90127-3 | MR 0322313 | Zbl 0255.34069
[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 0853276 | Zbl 0645.34027
[8] Müller-Pfeiffer, E.: Oscillation criteria of Nehari-type for Schrödinger equation. Math. Nachr. 96 (1980), 185-194. DOI 10.1002/mana.19800960116 | MR 0600809
[9] Myshkis, A. D.: Linear Differential Equations with Retarded Argument. Nauka, Moskva (1972), Russian. MR 0352648 | Zbl 0261.34040
[10] Nehari, Z.: Oscillation criteria for second-order linear differential equations. Trans. Amer. Math. Soc. 85 (1957), 428-445. DOI 10.1090/S0002-9947-1957-0087816-8 | MR 0087816 | Zbl 0078.07602
[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
[12] Partsvania, N.: On oscillation of solutions of second-order systems of deviated differential equations. Georgian Math. J. 3 (1996), 571-582. DOI 10.1007/BF02259985 | MR 1419836 | Zbl 0868.34054
[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 1632394
[15] Řehák, P.: Half-linear dynamic equations on time scales: IVP and oscillatory properties. Nonlinear Funct. Anal. Appl. 7 (2002), 361-403. MR 1946469 | Zbl 1037.34002
[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 10.1006/jmaa.2000.7124 | MR 1800179
[17] Swanson, C. A.: Comparison and Oscillation Theory of Linear Differential Equations. Academic Press, New York (1968). MR 0463570 | Zbl 0191.09904
[18] Willett, D.: Classification of second order linear differential equations with respect to oscillation. Adv. Math. 3 (1969), 594-623. DOI 10.1016/0001-8708(69)90011-5 | MR 0280800 | Zbl 0188.40101
[19] Wintner, A.: On the non-existence of conjugate points. Amer. J. Math. 73 (1951), 368-380. DOI 10.2307/2372182 | MR 0042005
Search
Partner of
