Oscillation of solutions of non-linear neutral delay differential equations of higher order for p ( t ) = ± 1

Radhanath N. Rath; Laxmi N. Padhy; Niyati Misra

Archivum Mathematicum (2004)

  • Volume: 040, Issue: 4, page 359-366
  • ISSN: 0044-8753

Abstract

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In this paper, the oscillation criteria for solutions of the neutral delay differential equation (NDDE) y ( t ) - p ( t ) y ( t - τ ) ( n ) + α Q ( t ) G y ( t - σ ) = f ( t ) has been studied where p ( t ) = 1 or p ( t ) ≤ 0 , α = ± 1 , Q ∈ C [ 0 , ∞ ) , R + , f ∈ C ( [ 0 , ∞ ) , R ) , G ∈ C ( R , R ) . This work improves and generalizes some recent results and answer some questions that are raised in [1].

How to cite

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Rath, Radhanath N., Padhy, Laxmi N., and Misra, Niyati. "Oscillation of solutions of non-linear neutral delay differential equations of higher order for $p(t)=\pm 1$." Archivum Mathematicum 040.4 (2004): 359-366. <http://eudml.org/doc/249317>.

@article{Rath2004,
abstract = {In this paper, the oscillation criteria for solutions of the neutral delay differential equation (NDDE) \[ \left( \{y(t)-p(t)\, y(\{t-\tau \} )\} \right)^\{(n )\}+ \alpha \,Q(t)\,\,G\left( \{y(\{t-\sigma \})\} \right)= f(t) \] has been studied where $p(t) = 1$ or $p(t) \le 0$, $\alpha =\pm 1$, $Q\in C \left([0, \infty ), R^\{+\}\right)$, $f \in C([0, \infty ), R)$, $G \in C(R, R)$. This work improves and generalizes some recent results and answer some questions that are raised in [1].},
author = {Rath, Radhanath N., Padhy, Laxmi N., Misra, Niyati},
journal = {Archivum Mathematicum},
keywords = {oscillation; non-oscillation; neutral equations; asymptotic-behaviour; non-oscillation; neutral equations; asymptotic-behaviour},
language = {eng},
number = {4},
pages = {359-366},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Oscillation of solutions of non-linear neutral delay differential equations of higher order for $p(t)=\pm 1$},
url = {http://eudml.org/doc/249317},
volume = {040},
year = {2004},
}

TY - JOUR
AU - Rath, Radhanath N.
AU - Padhy, Laxmi N.
AU - Misra, Niyati
TI - Oscillation of solutions of non-linear neutral delay differential equations of higher order for $p(t)=\pm 1$
JO - Archivum Mathematicum
PY - 2004
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 040
IS - 4
SP - 359
EP - 366
AB - In this paper, the oscillation criteria for solutions of the neutral delay differential equation (NDDE) \[ \left( {y(t)-p(t)\, y({t-\tau } )} \right)^{(n )}+ \alpha \,Q(t)\,\,G\left( {y({t-\sigma })} \right)= f(t) \] has been studied where $p(t) = 1$ or $p(t) \le 0$, $\alpha =\pm 1$, $Q\in C \left([0, \infty ), R^{+}\right)$, $f \in C([0, \infty ), R)$, $G \in C(R, R)$. This work improves and generalizes some recent results and answer some questions that are raised in [1].
LA - eng
KW - oscillation; non-oscillation; neutral equations; asymptotic-behaviour; non-oscillation; neutral equations; asymptotic-behaviour
UR - http://eudml.org/doc/249317
ER -

References

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  1. Gyori I., Ladas G., Oscillation Theory of Delay Differential Equations with Applications, Clarendon Press, Oxford, 1991. (1991) MR1168471
  2. Hilderbrandt T. H., Introduction to the Theory of Integration, Academic Press, New York, 1963. (1963) MR0154957
  3. Ladde G. S., Lakshmikantham V., Zhang B. G., Oscillation Theory of Differential Equations with Deviating Arguments, Marcel Dekker INC, New York, 1987. (1987) Zbl0832.34071MR1017244
  4. Liu X. Z., al, Oscillation and non-oscillation for a class of neutral differential equations, Differential Equations Dynam. Systems 1 (1993), 197–204. (1993) MR1258897
  5. Malik S. C., Arora S., Mathematical Analysis, New Age International (p) Ltd. Publishers New Delhi, 2001. 
  6. Parhi N., Rath R. N., On oscillation and asymptotic behaviour of solutions of forced first order neutral differential equations, Proc. Indian Acad. Sci. (Math. Sci.) 111 (2001), 337–350. Zbl0995.34058MR1851095
  7. Parhi N., Rath R. N., On oscillation of solutions of forced non-linear neutral differential equations of higher order – II, Ann. Polon. Math. 81 (2003), 101–110. MR1976190
  8. Parhi N., Rath R. N., Oscillatory behaviour of solutions of non-linear higher order neutral differential equations, Math. Bohem. 129 (2004), 11–27. MR2048783
  9. Rath R. N., Oscillatory and asymptotic behaviour of solutions of higher order neutral equations, Bull. Inst. Math. Acad. Sinica 30 (2003), 219–228. MR1922656
  10. Yu J. S., al, Oscillation of neutral delay differential equation, Bull. Austral. Math. Soc. 45 (1992), 195–200. (1992) 

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