On oscillation of solutions of forced nonlinear neutral differential equations of higher order

N. Parhi; Radhanath N. Rath

Czechoslovak Mathematical Journal (2003)

  • Volume: 53, Issue: 4, page 805-825
  • ISSN: 0011-4642

Abstract

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In this paper, necessary and sufficient conditions are obtained for every bounded solution of [ y ( t ) - p ( t ) y ( t - τ ) ] ( n ) + Q ( t ) G y ( t - σ ) = f ( t ) , t ≥ 0 , ( * ) to oscillate or tend to zero as t → ∞ for different ranges of p ( t ) . It is shown, under some stronger conditions, that every solution of ( * ) oscillates or tends to zero as t → ∞ . Our results hold for linear, a class of superlinear and other nonlinear equations and answer a conjecture by Ladas and Sficas, Austral. Math. Soc. Ser. B 27 (1986), 502–511, and generalize some known results.

How to cite

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Parhi, N., and Rath, Radhanath N.. "On oscillation of solutions of forced nonlinear neutral differential equations of higher order." Czechoslovak Mathematical Journal 53.4 (2003): 805-825. <http://eudml.org/doc/30817>.

@article{Parhi2003,
abstract = {In this paper, necessary and sufficient conditions are obtained for every bounded solution of \[ [y (t) - p (t) y (t - \tau )]^\{(n)\} + Q (t) G \bigl (y (t - \sigma )\bigr ) = f (t), \quad t \ge 0, \qquad \mathrm \{(*)\}\] to oscillate or tend to zero as $t \rightarrow \infty $ for different ranges of $p (t)$. It is shown, under some stronger conditions, that every solution of $(*)$ oscillates or tends to zero as $t \rightarrow \infty $. Our results hold for linear, a class of superlinear and other nonlinear equations and answer a conjecture by Ladas and Sficas, Austral. Math. Soc. Ser. B 27 (1986), 502–511, and generalize some known results.},
author = {Parhi, N., Rath, Radhanath N.},
journal = {Czechoslovak Mathematical Journal},
keywords = {oscillation; nonoscillation; neutral equations; asymptotic behaviour; oscillation; nonoscillation; neutral equations; asymptotic behaviour},
language = {eng},
number = {4},
pages = {805-825},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On oscillation of solutions of forced nonlinear neutral differential equations of higher order},
url = {http://eudml.org/doc/30817},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Parhi, N.
AU - Rath, Radhanath N.
TI - On oscillation of solutions of forced nonlinear neutral differential equations of higher order
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 4
SP - 805
EP - 825
AB - In this paper, necessary and sufficient conditions are obtained for every bounded solution of \[ [y (t) - p (t) y (t - \tau )]^{(n)} + Q (t) G \bigl (y (t - \sigma )\bigr ) = f (t), \quad t \ge 0, \qquad \mathrm {(*)}\] to oscillate or tend to zero as $t \rightarrow \infty $ for different ranges of $p (t)$. It is shown, under some stronger conditions, that every solution of $(*)$ oscillates or tends to zero as $t \rightarrow \infty $. Our results hold for linear, a class of superlinear and other nonlinear equations and answer a conjecture by Ladas and Sficas, Austral. Math. Soc. Ser. B 27 (1986), 502–511, and generalize some known results.
LA - eng
KW - oscillation; nonoscillation; neutral equations; asymptotic behaviour; oscillation; nonoscillation; neutral equations; asymptotic behaviour
UR - http://eudml.org/doc/30817
ER -

References

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Citations in EuDML Documents

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  1. N. Parhi, Arun Kumar Tripathy, On oscillatory fourth order nonlinear neutral differential equations. I.
  2. N. Parhi, Radhanath N. Rath, Oscillatory behaviour of solutions of nonlinear higher order neutral differential equations
  3. N. Parhi, Arun Kumar Tripathy, On oscillatory fourth order nonlinear neutral differential equations. II.
  4. R.N. Rath, K.C. Panda, S.K. Rath, Oscillatory behavior of higher order neutral differential equation with multiple functional delays under derivative operator
  5. N. Parhi, Radhanath N. Rath, On oscillation criteria for forced nonlinear higher order neutral differential equations
  6. Julio G. Dix, Dillip Kumar Ghose, Radhanath Rath, Oscillation of a higher order neutral differential equation with a sub-linear delay term and positive and negative coefficients

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