Oscillation results for second order nonlinear differential equations

Jozef Džurina; Dáša Lacková

Open Mathematics (2004)

  • Volume: 2, Issue: 1, page 57-66
  • ISSN: 2391-5455

Abstract

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In this paper, the authors present some new results for the oscillation of the second order nonlinear neutral differential equations of the form r t ψ x t x t + p t x τ t ' ' + q t f x σ t = 0 . Easily verifiable criteria are obtained that are also new for differential equations without neutral term i.e. for p(t)≡0.

How to cite

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Jozef Džurina, and Dáša Lacková. "Oscillation results for second order nonlinear differential equations." Open Mathematics 2.1 (2004): 57-66. <http://eudml.org/doc/268725>.

@article{JozefDžurina2004,
abstract = {In this paper, the authors present some new results for the oscillation of the second order nonlinear neutral differential equations of the form \[\left( \{r\left( t \right)\psi \left( \{x\left( t \right)\} \right)\left[ \{x\left( t \right) + p\left( t \right)x\left( \{\tau \left( t \right)\} \right)\} \right]^\prime \} \right)^\prime + q\left( t \right)f\left( \{x\left[ \{\sigma \left( t \right)\} \right]\} \right) = 0\] . Easily verifiable criteria are obtained that are also new for differential equations without neutral term i.e. for p(t)≡0.},
author = {Jozef Džurina, Dáša Lacková},
journal = {Open Mathematics},
keywords = {34C10},
language = {eng},
number = {1},
pages = {57-66},
title = {Oscillation results for second order nonlinear differential equations},
url = {http://eudml.org/doc/268725},
volume = {2},
year = {2004},
}

TY - JOUR
AU - Jozef Džurina
AU - Dáša Lacková
TI - Oscillation results for second order nonlinear differential equations
JO - Open Mathematics
PY - 2004
VL - 2
IS - 1
SP - 57
EP - 66
AB - In this paper, the authors present some new results for the oscillation of the second order nonlinear neutral differential equations of the form \[\left( {r\left( t \right)\psi \left( {x\left( t \right)} \right)\left[ {x\left( t \right) + p\left( t \right)x\left( {\tau \left( t \right)} \right)} \right]^\prime } \right)^\prime + q\left( t \right)f\left( {x\left[ {\sigma \left( t \right)} \right]} \right) = 0\] . Easily verifiable criteria are obtained that are also new for differential equations without neutral term i.e. for p(t)≡0.
LA - eng
KW - 34C10
UR - http://eudml.org/doc/268725
ER -

References

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  1. [1] D.D. Bainov and D.P. Mishev: Oscillation Theory for Neutral Differential Equations with Delay, Adam Hilger, Bristol, Philadelphia, New York, 1991. 
  2. [2] M. Budincevic: “Oscillation of second order neutral nonlinear differential equations”, Novi Sad J. Math., Vol. 27, (1997), pp. 49–56. Zbl1074.34500
  3. [3] T.A. Chanturija and I.T. Kiguradze: Asymptotic properties of solutions of nonautonomous ordinary differential equations. Nauka, Moscow, 1991. (Russian) 
  4. [4] L.H. Erbe, Q. Kong, B.G. Zhang: Oscillation Theory for Functional Differential Equations, Adam Hilger, New York, Basel, Hong Kong, 1991. 
  5. [5] L.H. Erbe and Q. Kong: “Oscillation résults for second order neutral differential equations”, Funk. Ekvacioj, Vol. 35, (1992), pp. 545–557. Zbl0787.34057
  6. [6] Q. Chuanxi and G. Ladas: “Oscillations of higher order neutral differential equations with variable coefficients”, Math. Nachr., Vol. 150, (1991), pp. 15–24. Zbl0728.34075
  7. [7] S.R. Grace and B.S. Lalli: “Oscillation and asymptotic behavior of certain second order neutral differential equations”, Radovi Mat., Vol. 5, (1989), pp. 121–126. Zbl0677.34058
  8. [8] M.K. Grammatikopoulos, G. Ladas and A. Meimaridou: “Oscillation and asymptotic behavior of higher order neutral equations with variable coefficients”, Chin. Ann. of Math., Vol. 9B, (1988), pp. 322–338. Zbl0672.34066
  9. [9] K. Gopalsamy, B.S. Lalli and B.G. Zhang: “Oscillation of odd order neutral differential equations”, Czech. Math. J., Vol. 42, (1992), pp. 313–323. Zbl0778.34050
  10. [10] I. Győri and G. Ladas: Theory of Delay Differential Equations with Applications, Clarendon Press, Oxford, (1991). Zbl0780.34048
  11. [11] J. Hale: Theory of functional differential equations, Springer-Verlag, New York, 1977. Zbl0352.34001
  12. [12] N. Parhi and P.K. Mohanty: “Oscillation of neutral differential equations of higher order”, Bull. Inst. Math. Sinica, Vol. 24, (1996), pp. 139–150. Zbl0858.34059
  13. [13] M. Ružičková and E. Špániková: “Comparison theorems for differential equations of neutral type”, Fasc. Math., Vol. 128, (1998), pp. 141–148. Zbl0915.34068
  14. [14] P. Wang, Y. Yu: “Oscillation of second order order neutral equations with deviating argument”, Math. J. Toyama Univ., Vol. 21, (1998), pp. 55–66. Zbl0983.34058

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