Oscillation criteria for a class of nonlinear differential equations of third order
N. Parhi ; P. Das
Annales Polonici Mathematici, Tome 57 (1992), p. 219-229 / Harvested from The Polish Digital Mathematics Library

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

Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:275914
@article{bwmeta1.element.bwnjournal-article-apmv57z3p219bwm,
     author = {N. Parhi and P. Das},
     title = {Oscillation criteria for a class of nonlinear differential equations of third order},
     journal = {Annales Polonici Mathematici},
     volume = {57},
     year = {1992},
     pages = {219-229},
     zbl = {0771.34024},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv57z3p219bwm}
}
N. Parhi; P. Das. Oscillation criteria for a class of nonlinear differential equations of third order. Annales Polonici Mathematici, Tome 57 (1992) pp. 219-229. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv57z3p219bwm/

[000] [1] L. Erbe, Oscillation, nonoscillation and asymptotic behaviour for third order nonlinear differential equations, Ann. Mat. Pura Appl. 110 (1976), 373-393.

[001] [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. | Zbl 0645.34026

[002] [3] J. W. Heidel, Qualitative behaviour of solutions of a third order nonlinear differential equation, Pacific J. Math. 27 (1968), 507-526.

[003] [4] T. Kura, Nonoscillation criteria for nonlinear ordinary differential equations of the third order, Nonlinear Anal. 8 (1984), 369-379. | Zbl 0539.34024

[004] [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. | Zbl 0143.31501

[005] [6] J. L. Nelson, A stability theorem for a third order nonlinear differential equation, Pacific J. Math. 24 (1968), 341-344. | Zbl 0155.13901

[006] [7] N. Parhi, Nonoscillatory behaviour of solutions of nonhomogeneous third order differential equations, Appl. Anal. 12 (1981), 273-285. | Zbl 0478.34030

[007] [8] N. Parhi, Nonoscillation of solutions of a class of third order differential equations, Acta Math. Acad. Sci. Hungar. 54 (1989), 79-88. | Zbl 0685.34031

[008] [9] N. Parhi and S. K. Nayak, Nonoscillation of second order nonhomogeneous differential equations, J. Math. Anal. Appl. 102 (1984), 62-74. | Zbl 0544.34025

[009] [10] N. Parhi and S. Parhi, On the behaviour of solutions of the differential equation (r(t)y'')'+q(t)(y')β+p(t)yα=f(t), Ann. Polon. Math. 47 (1986), 137-148. | Zbl 0628.34036

[010] [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. | Zbl 0685.34032

[011] [12] C. A. Swanson, Comparison and Oscillation Theory of Linear Differential Equations, Academic Press, New York 1968.

[012] [13] P. Waltman, Oscillation criteria for third order nonlinear differential equations, Pacific J. Math. 18 (1966), 385-389. | Zbl 0144.11403