Oscillation of unstable second order neutral differential equations with mixed argument

Jozef Džurina; Viktor Pirč

Mathematica Bohemica (2005)

  • Volume: 130, Issue: 3, page 323-333
  • ISSN: 0862-7959

Abstract

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The aim of this paper is to present new oscillatory criteria for the second order neutral differential equation with mixed argument ( x ( t ) - p x ( t - τ ) ) ' ' - q ( t ) x ( σ ( t ) ) = 0 . The results include also sufficient conditions for bounded and unbounded oscillation of the equations considered.

How to cite

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Džurina, Jozef, and Pirč, Viktor. "Oscillation of unstable second order neutral differential equations with mixed argument." Mathematica Bohemica 130.3 (2005): 323-333. <http://eudml.org/doc/249580>.

@article{Džurina2005,
abstract = {The aim of this paper is to present new oscillatory criteria for the second order neutral differential equation with mixed argument \[ (x(t)-px(t-\tau ))^\{\prime \prime \}- q(t)x(\sigma (t))=0. \] The results include also sufficient conditions for bounded and unbounded oscillation of the equations considered.},
author = {Džurina, Jozef, Pirč, Viktor},
journal = {Mathematica Bohemica},
keywords = {neutral equation; mixed argument; neutral equation},
language = {eng},
number = {3},
pages = {323-333},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillation of unstable second order neutral differential equations with mixed argument},
url = {http://eudml.org/doc/249580},
volume = {130},
year = {2005},
}

TY - JOUR
AU - Džurina, Jozef
AU - Pirč, Viktor
TI - Oscillation of unstable second order neutral differential equations with mixed argument
JO - Mathematica Bohemica
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 130
IS - 3
SP - 323
EP - 333
AB - The aim of this paper is to present new oscillatory criteria for the second order neutral differential equation with mixed argument \[ (x(t)-px(t-\tau ))^{\prime \prime }- q(t)x(\sigma (t))=0. \] The results include also sufficient conditions for bounded and unbounded oscillation of the equations considered.
LA - eng
KW - neutral equation; mixed argument; neutral equation
UR - http://eudml.org/doc/249580
ER -

References

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  1. Oscillation Theory for Neutral Differential Equations with Delay, Adam Hilger, 1991. (1991) MR1147908
  2. On Oscillatory Properties of Differential Equations with Deviating Arguments, Tbilisi, Univ. Press, Tbilisi, 1977. (Russian) (1977) 
  3. A note on unstable neutral differential equations of the second order, Math. Fascic. 29 (1999), 17–22. (1999) MR1724462
  4. Oscillation Theory for Functional Differential Equations, Marcel Dekker, New York, 1995. (1995) MR1309905
  5. Theory of Delay Differential Equations with Applications, Clarendon Press, Oxford, 1991. (1991) MR1168471
  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 and bounded oscillation for second-order neutral differential equations of unstable type, J. Syst. Sci. Math. 16 (1996), 92–96. (1996) MR1404160
  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) Zbl0754.34075MR1159633DOI10.1016/0022-247X(92)90322-5

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