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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.
Rocznik
Tom
57
Numer
3
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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