# Oscillation results for second order nonlinear differential equations

Open Mathematics (2004)

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

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topJozef 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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- [10] I. Győri and G. Ladas: Theory of Delay Differential Equations with Applications, Clarendon Press, Oxford, (1991). Zbl0780.34048
- [11] J. Hale: Theory of functional differential equations, Springer-Verlag, New York, 1977. Zbl0352.34001
- [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] M. Ružičková and E. Špániková: “Comparison theorems for differential equations of neutral type”, Fasc. Math., Vol. 128, (1998), pp. 141–148. Zbl0915.34068
- [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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