Oscillation of the third order Euler differential equation with delay

Blanka Baculíková; Jozef Džurina

Mathematica Bohemica (2014)

  • Volume: 139, Issue: 4, page 649-655
  • ISSN: 0862-7959

Abstract

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In the paper we offer criteria for oscillation of the third order Euler differential equation with delay y ' ' ' ( t ) + k 2 t 3 y ( c t ) = 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.

How to cite

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Baculíková, Blanka, and Džurina, Jozef. "Oscillation of the third order Euler differential equation with delay." Mathematica Bohemica 139.4 (2014): 649-655. <http://eudml.org/doc/269857>.

@article{Baculíková2014,
abstract = {In the paper we offer criteria for oscillation of the third order Euler differential equation with delay \[ y^\{\prime \prime \prime \}(t)+\frac\{k^2\}\{t^3\}y(ct)=0. \] 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.},
author = {Baculíková, Blanka, Džurina, Jozef},
journal = {Mathematica Bohemica},
keywords = {third-order functional differential equation; Euler equation; oscillation; nonoscillation; oscillation; nonoscillation; Euler equation; delay},
language = {eng},
number = {4},
pages = {649-655},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillation of the third order Euler differential equation with delay},
url = {http://eudml.org/doc/269857},
volume = {139},
year = {2014},
}

TY - JOUR
AU - Baculíková, Blanka
AU - Džurina, Jozef
TI - Oscillation of the third order Euler differential equation with delay
JO - Mathematica Bohemica
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 139
IS - 4
SP - 649
EP - 655
AB - In the paper we offer criteria for oscillation of the third order Euler differential equation with delay \[ y^{\prime \prime \prime }(t)+\frac{k^2}{t^3}y(ct)=0. \] 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.
LA - eng
KW - third-order functional differential equation; Euler equation; oscillation; nonoscillation; oscillation; nonoscillation; Euler equation; delay
UR - http://eudml.org/doc/269857
ER -

References

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  2. Baculíková, B., Properties of third-order nonlinear functional differential equations with mixed arguments, Abstr. Appl. Anal. 2011 (2011), Article No. 857860, 15 pages. (2011) Zbl1217.34109MR2776748
  3. Cecchi, M., Došlá, Z., Marini, M., 10.1006/jmaa.1998.6247, J. Math. Anal. Appl. 231 (1999), Article ID jmaa.1998.6247, 509-525. (1999) MR1669163DOI10.1006/jmaa.1998.6247
  4. Džurina, J., Asymptotic properties of third order delay differential equations, Czech. Math. J. 45 (1995), 443-448. (1995) MR1344509
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  6. Kiguradze, I. T., Chanturia, T. A., 10.1007/978-94-011-1808-8, Mathematics and Its Applications (Soviet Series) 89 Kluwer Academic Publishers, Dordrecht (1993), translated from the 1985 Russian original. (1993) Zbl0782.34002MR1220223DOI10.1007/978-94-011-1808-8
  7. Kulenović, M. R. S., Oscillation of the Euler differential equation with delay, Czech. Math. J. 45 (1995), 1-6. (1995) Zbl0832.34069MR1314527
  8. Kusano, T., Naito, M., 10.2969/jmsj/03330509, J. Math. Soc. Japan 33 (1981), 509-532. (1981) Zbl0494.34049MR0620288DOI10.2969/jmsj/03330509
  9. Kusano, T., Naito, M., Tanaka, K., 10.1017/S0308210500015328, Proc. R. Soc. Edinb., Sect. A, Math. 90 (1981), 25-40. (1981) Zbl0486.34021MR0636062DOI10.1017/S0308210500015328
  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). (1987) Zbl0832.34071MR1017244

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