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Keywords:
third-order functional differential equation; Euler equation; oscillation; nonoscillation
third-order functional differential equation; Euler equation; oscillation; nonoscillation
Summary:
In the paper we offer criteria for oscillation of the third order Euler differential equation with delay $$ y'''(t)+\frac {k^2}{t^3}y(ct)=0. $$ We provide detail analysis of the properties of this equation, we fill the gap in the oscillation theory and provide necessary and sufficient conditions for oscillation of equation considered.
References:
[1] Arino, O., Győri, I.: Necessary and sufficient condition for oscillation of a neutral differential system with several delays. J. Differ. Equations 81 (1989), 98-105. DOI 10.1016/0022-0396(89)90179-4 | MR 1012201 | Zbl 0691.34054
[2] Baculíková, B.: Properties of third-order nonlinear functional differential equations with mixed arguments. Abstr. Appl. Anal. 2011 (2011), Article No. 857860, 15 pages. MR 2776748 | Zbl 1217.34109
[3] Cecchi, M., Došlá, Z., Marini, M.: On third order differential equations with property A and B. J. Math. Anal. Appl. 231 (1999), Article ID jmaa.1998.6247, 509-525. DOI 10.1006/jmaa.1998.6247 | MR 1669163
[4] Džurina, J.: Asymptotic properties of third order delay differential equations. Czech. Math. J. 45 (1995), 443-448. MR 1344509
[5] Džurina, J.: Comparison theorems for differential equations with deviating argument. Math. Slovaca 45 (1995), 79-89. MR 1335843 | Zbl 0830.34059
[6] Kiguradze, I. T., Chanturia, T. A.: Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations. Mathematics and Its Applications (Soviet Series) 89 Kluwer Academic Publishers, Dordrecht (1993), translated from the 1985 Russian original. DOI 10.1007/978-94-011-1808-8 | MR 1220223 | Zbl 0782.34002
[7] Kulenović, M. R. S.: Oscillation of the Euler differential equation with delay. Czech. Math. J. 45 (1995), 1-6. MR 1314527 | Zbl 0832.34069
[8] Kusano, T., Naito, M.: Comparison theorems for functional-differential equations with deviating arguments. J. Math. Soc. Japan 33 (1981), 509-532. DOI 10.2969/jmsj/03330509 | MR 0620288 | Zbl 0494.34049
[9] Kusano, T., Naito, M., Tanaka, K.: Oscillatory and asymptotic behaviour of solutions of a class of linear ordinary differential equations. Proc. R. Soc. Edinb., Sect. A, Math. 90 (1981), 25-40. DOI 10.1017/S0308210500015328 | MR 0636062 | Zbl 0486.34021
[10] Ladde, G. S., Lakshmikantham, V., Zhang, B. G.: Oscillation Theory of Differential Equations with Deviating Arguments. Monographs and Textbooks in Pure and Applied Mathematics 110 Marcel Dekker, New York (1987). MR 1017244 | Zbl 0832.34071
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