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## Annales Polonici Mathematici

1992 | 57 | 3 | 219-229
Tytuł artykułu

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

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
EN
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
219-229
Opis fizyczny
Daty
wydano
1992
otrzymano
1990-09-01
poprawiono
1991-07-29
poprawiono
1992-05-15
Twórcy
autor
• Department of Mathematics, Berhampur University, Berhampur 760 007, India
autor
• Department of Mathematics, Berhampur University, Berhampur 760 007, India
Bibliografia
• [1] L. Erbe, Oscillation, nonoscillation and asymptotic behaviour for third order nonlinear differential equations, Ann. Mat. Pura Appl. 110 (1976), 373-393.
• [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.
• [3] J. W. Heidel, Qualitative behaviour of solutions of a third order nonlinear differential equation, Pacific J. Math. 27 (1968), 507-526.
• [4] T. Kura, Nonoscillation criteria for nonlinear ordinary differential equations of the third order, Nonlinear Anal. 8 (1984), 369-379.
• [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.
• [6] J. L. Nelson, A stability theorem for a third order nonlinear differential equation, Pacific J. Math. 24 (1968), 341-344.
• [7] N. Parhi, Nonoscillatory behaviour of solutions of nonhomogeneous third order differential equations, Appl. Anal. 12 (1981), 273-285.
• [8] N. Parhi, Nonoscillation of solutions of a class of third order differential equations, Acta Math. Acad. Sci. Hungar. 54 (1989), 79-88.
• [9] N. Parhi and S. K. Nayak, Nonoscillation of second order nonhomogeneous differential equations, J. Math. Anal. Appl. 102 (1984), 62-74.
• [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.
• [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.
• [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.
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Bibliografia
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