# Oscillation criteria for a class of nonlinear differential equations of third order

Annales Polonici Mathematici (1992)

- Volume: 57, Issue: 3, page 219-229
- ISSN: 0066-2216

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topN. Parhi, and P. Das. "Oscillation criteria for a class of nonlinear differential equations of third order." Annales Polonici Mathematici 57.3 (1992): 219-229. <http://eudml.org/doc/275914>.

@article{N1992,

abstract = {Oscillation criteria are obtained for nonlinear homogeneous third order differential equations of the form
$y^\{\prime \prime \prime \} + q(t)y^\{\prime \} + p(t)y^α = 0$
and
y”’ + q(t)y’ + p(t)f(y) = 0,
where p and q are real-valued continuous functions on [a,∞), f is a real-valued continuous function on (-∞, ∞) and α > 0 is a quotient of odd integers. Sign restrictions are imposed on p(t) and q(t). These results generalize some of the results obtained earlier in this direction.},

author = {N. Parhi, P. Das},

journal = {Annales Polonici Mathematici},

keywords = {third order equations; oscillation; nonoscillation; asymptotic behaviour; oscillation criteria; nonlinear differential equations},

language = {eng},

number = {3},

pages = {219-229},

title = {Oscillation criteria for a class of nonlinear differential equations of third order},

url = {http://eudml.org/doc/275914},

volume = {57},

year = {1992},

}

TY - JOUR

AU - N. Parhi

AU - P. Das

TI - Oscillation criteria for a class of nonlinear differential equations of third order

JO - Annales Polonici Mathematici

PY - 1992

VL - 57

IS - 3

SP - 219

EP - 229

AB - Oscillation criteria are obtained for nonlinear homogeneous third order differential equations of the form
$y^{\prime \prime \prime } + q(t)y^{\prime } + p(t)y^α = 0$
and
y”’ + q(t)y’ + p(t)f(y) = 0,
where p and q are real-valued continuous functions on [a,∞), f is a real-valued continuous function on (-∞, ∞) and α > 0 is a quotient of odd integers. Sign restrictions are imposed on p(t) and q(t). These results generalize some of the results obtained earlier in this direction.

LA - eng

KW - third order equations; oscillation; nonoscillation; asymptotic behaviour; oscillation criteria; nonlinear differential equations

UR - http://eudml.org/doc/275914

ER -

## References

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- [2] L. H. Erbe and V. S. H. Rao, Nonoscillation results for third order nonlinear differential equations, J. Math. Anal. Appl. 125 (1987), 471-482. Zbl0645.34026
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- [9] N. Parhi and S. K. Nayak, Nonoscillation of second order nonhomogeneous differential equations, J. Math. Anal. Appl. 102 (1984), 62-74. Zbl0544.34025
- [10] N. Parhi and S. Parhi, On the behaviour of solutions of the differential equation ${\left(r\left(t\right){y}^{\text{'}\text{'}}\right)}^{\text{'}}+q\left(t\right){\left({y}^{\text{'}}\right)}^{\beta}+p\left(t\right){y}^{\alpha}=f\left(t\right)$, Ann. Polon. Math. 47 (1986), 137-148. Zbl0628.34036
- [11] N. Parhi and S. Parhi, Qualitative behaviour of solutions of forced nonlinear third order differential equations, Riv. Mat. Univ. Parma 13 (1987), 201-210. Zbl0685.34032
- [12] C. A. Swanson, Comparison and Oscillation Theory of Linear Differential Equations, Academic Press, New York 1968.
- [13] P. Waltman, Oscillation criteria for third order nonlinear differential equations, Pacific J. Math. 18 (1966), 385-389. Zbl0144.11403

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