On unstable neutral differential equations of the second order

Jozef Džurina

Czechoslovak Mathematical Journal (2002)

  • Volume: 52, Issue: 4, page 739-747
  • ISSN: 0011-4642

Abstract

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The aim of this paper is to present sufficient conditions for all bounded solutions of the second order neutral differential equation ( x ( t ) - p x ( t - τ ) ) ' ' - q ( t ) x ( σ ( t ) ) = 0 to be oscillatory and to improve some existing results. The main results are based on the comparison principles.

How to cite

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Džurina, Jozef. "On unstable neutral differential equations of the second order." Czechoslovak Mathematical Journal 52.4 (2002): 739-747. <http://eudml.org/doc/30740>.

@article{Džurina2002,
abstract = {The aim of this paper is to present sufficient conditions for all bounded solutions of the second order neutral differential equation \[ \big (x(t)-px(t-\tau )\big )^\{\prime \prime \}- q(t)x\big (\sigma (t)\big )=0 \] to be oscillatory and to improve some existing results. The main results are based on the comparison principles.},
author = {Džurina, Jozef},
journal = {Czechoslovak Mathematical Journal},
keywords = {neutral equation; delayed argument; neutral equation; delayed argument},
language = {eng},
number = {4},
pages = {739-747},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On unstable neutral differential equations of the second order},
url = {http://eudml.org/doc/30740},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Džurina, Jozef
TI - On unstable neutral differential equations of the second order
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 4
SP - 739
EP - 747
AB - The aim of this paper is to present sufficient conditions for all bounded solutions of the second order neutral differential equation \[ \big (x(t)-px(t-\tau )\big )^{\prime \prime }- q(t)x\big (\sigma (t)\big )=0 \] to be oscillatory and to improve some existing results. The main results are based on the comparison principles.
LA - eng
KW - neutral equation; delayed argument; neutral equation; delayed argument
UR - http://eudml.org/doc/30740
ER -

References

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  1. Oscillation Theory for Neutral Differential Equations with Delay, Adam Hilger, Bristol, 1991. (1991) MR1147908
  2. On oscillatory properties of differential equations with deviating arguments, Tbilisi, Univ. Press, Tbilisi, 1977. (Russian) (1977) 
  3. Oscillation Theory for Functional Differential Equations, Dekker, New York, 1995. (1995) MR1309905
  4. Theory of Delay Differential Equations with Applications, Clarendon Press, Oxford, 1991. (1991) MR1168471
  5. 10.4099/math1924.15.415, Japan. J. Math. 15 (1989), 415–432. (1989) MR1039249DOI10.4099/math1924.15.415
  6. Oscillation theory of differential equations with deviating arguments, Dekker, New York, 1987. (1987) MR1017244
  7. 10.1017/S0004972700011758, Bull. Austral. Math. Soc. 46 (1992), 149–157. (1992) MR1170449DOI10.1017/S0004972700011758
  8. The existence of positive solution for second order neutral differential equations with unstable type, Systems Sci. Math. Sci (to appear). (to appear) 
  9. Oscillation of second order neutral differential equations, Kexue Tongbao 34 (1989), 563–566. (1989) Zbl0661.34074MR1020422
  10. 10.1016/0022-247X(92)90322-5, J. Math. Anal. Appl. 166 (1992), 1–11. (1992) MR1159633DOI10.1016/0022-247X(92)90322-5

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