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

N. Parhi; P. Das

Annales Polonici Mathematici (1992)

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

Abstract

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Oscillation criteria are obtained for nonlinear homogeneous third order differential equations of the form y ' ' ' + q ( t ) y ' + 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.

How to cite

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N. 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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  1. [1] L. Erbe, Oscillation, nonoscillation and asymptotic behaviour for third order nonlinear differential equations, Ann. Mat. Pura Appl. 110 (1976), 373-393. 
  2. [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
  3. [3] J. W. Heidel, Qualitative behaviour of solutions of a third order nonlinear differential equation, Pacific J. Math. 27 (1968), 507-526. 
  4. [4] T. Kura, Nonoscillation criteria for nonlinear ordinary differential equations of the third order, Nonlinear Anal. 8 (1984), 369-379. Zbl0539.34024
  5. [5] A. C. Lazer, The behaviour of solutions of the differential equation y''' + p(x)y' + q(x)y = 0, Pacific J. Math. 17 (1966), 435-466. Zbl0143.31501
  6. [6] J. L. Nelson, A stability theorem for a third order nonlinear differential equation, Pacific J. Math. 24 (1968), 341-344. Zbl0155.13901
  7. [7] N. Parhi, Nonoscillatory behaviour of solutions of nonhomogeneous third order differential equations, Appl. Anal. 12 (1981), 273-285. Zbl0478.34030
  8. [8] N. Parhi, Nonoscillation of solutions of a class of third order differential equations, Acta Math. Acad. Sci. Hungar. 54 (1989), 79-88. Zbl0685.34031
  9. [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. [10] N. Parhi and S. Parhi, On the behaviour of solutions of the differential equation ( r ( t ) y ' ' ) ' + q ( t ) ( y ' ) β + p ( t ) y α = f ( t ) , Ann. Polon. Math. 47 (1986), 137-148. Zbl0628.34036
  11. [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. [12] C. A. Swanson, Comparison and Oscillation Theory of Linear Differential Equations, Academic Press, New York 1968. 
  13. [13] P. Waltman, Oscillation criteria for third order nonlinear differential equations, Pacific J. Math. 18 (1966), 385-389. Zbl0144.11403

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