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

Czechoslovak Mathematical Journal (2003)

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

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topParhi, 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

top- Oscillation and asymptotic behaviour of higher order neutral differential equations, Bull. Inst. Math. Acad. Sinica 22 (1994), 203–217. (1994) MR1297358
- 10.1002/mana.19911500103, Math. Nachr. 150 (1991), 15–24. (1991) MR1109642DOI10.1002/mana.19911500103
- 10.1155/S0161171291000923, Internat. J. Math. Math. Sci. 14 (1991), 689–696. (1991) MR1125418DOI10.1155/S0161171291000923
- Oscillation in odd order neutral differential equations, Czechoslovak Math. J. 42 (1992), 313–323. (1992) MR1179502
- Oscillation of even order neutral differential equations, Indian J. Math. 35 (1993), 9–25. (1993) MR1249639
- 10.1006/jmaa.1996.0334, J. Math. Anal. Appl. 202 (1996), 555–577. (1996) MR1406248DOI10.1006/jmaa.1996.0334
- Oscialltion Theory of Delay-Differential Equations with Applications, Clarendon Press, Oxford, 1991. (1991) MR1168471
- Introduction to the Theory of Integration, Academic Press, New York, 1963. (1963) Zbl0112.28302MR0154957
- On the oscillation of solutions of the equation $\frac{{\mathrm{d}}^{m}u}{\mathrm{d}{t}^{m}}+a\left(t\right){u}^{m}u=0$, Mat. Sb. 65 (1964), 172–187. (1964) MR0173060
- 10.1017/S0334270000005105, Austral. Math. Soc. Ser. B 27 (1986), 502–511. (1986) MR0836222DOI10.1017/S0334270000005105
- Oscillations of higher order neutral differential equations, Portugal. Math. 48 (1991), 291–307. (1991) MR1127127
- Oscillation Theory of Differential Equations with Deviating Arguments, Marcel Dekker INC., New York, 1987. (1987) MR1017244
- Oscillation and nonoscillation for a class of neutral differential equations, Differential Equations Dynam. Systems 1 (1993), 197–204. (1993) MR1258897
- Oscillation of solutions of forced neutral differential equations of $n$-th order, Czechoslovak Math. J. 45 (1995), 413–433. (1995) MR1344507
- Maintenance of oscillation of neutral differential equations under the effect of a forcing term, Indian J. Pure Appl. Math. 26 (1995), 909–919. (1995) MR1347539
- Oscillatory behaviour of solutions of forced neutral differential equations, Ann. Polon. Math. 65 (1996), 1–10. (1996) MR1414747
- Oscillations of neutral differential equations of higher order, Bull. Inst. Math. Acad. Sinica 24 (1996), 139–150. (1996) MR1398241
- 10.1023/A:1022405707349, Czechoslovak Math. J. 50 (2000), 155–173. (2000) DOI10.1023/A:1022405707349
- On oscillation criteria for a forced neutral differential equation, Bull. Inst. Math. Acad. Sinica 28 (2000), 59–70. (2000) MR1750329
- 10.1006/jmaa.2000.7315, J. Math. Anal. Appl. 256 (2001), 525–541. (2001) MR1821755DOI10.1006/jmaa.2000.7315
- On oscillation and asymptotic behaviour of solutions of forced first order neutral differential equations, Proc. Indian. Acad. Sci. (Math. Sci.), Vol. 111, 2001, pp. 337–350. (2001) MR1851095
- Real Analysis, 3rd edition, MacMillan Publ. Co., New York, 1989. (1989) MR1013117
- 10.1006/jmaa.1996.0262, J. Math. Anal. Appl. 201 (1996), 387–395. (1996) Zbl0860.34040MR1396907DOI10.1006/jmaa.1996.0262
- Oscillation of higher order nonlinear neutral functional differential equation, Ann. Differential Equations 12 (1996), 83–88. (1996) Zbl0849.34059MR1394017
- Oscillation of higher order neutral differential equations, Rocky Mountain J. Math (to appear). (to appear) MR1340027
- Oscillations and nonoscillations in higher order neutral equations, J. Math. Phys. Sci. 25 (1991), 152–165. (1991)

## Citations in EuDML Documents

top- N. Parhi, Arun Kumar Tripathy, On oscillatory fourth order nonlinear neutral differential equations. I.
- N. Parhi, Radhanath N. Rath, Oscillatory behaviour of solutions of nonlinear higher order neutral differential equations
- N. Parhi, Arun Kumar Tripathy, On oscillatory fourth order nonlinear neutral differential equations. II.
- N. Parhi, Radhanath N. Rath, On oscillation criteria for forced nonlinear higher order neutral differential equations
- 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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