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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Asymptotic property of solutions of a class of third-order differential equations

Authors: N. Parhi and P. Das
Journal: Proc. Amer. Math. Soc. 110 (1990), 387-393
MSC: Primary 34C10; Secondary 34E05
MathSciNet review: 1019279
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Abstract: It has been shown that the equation (*)

$\displaystyle y''' + a(t)y'' + b(t)y' + c(t)y = 0,$

where $ a,b$, and $ c$ are real-valued continuous functions on $ [\alpha ,\infty )$ such that $ a(t) \geq 0,b(t) \leq 0$, and $ c(t) > 0$, admits at most one solution $ y(t)$ (neglecting linear dependence) with the property $ y(t)y'(t) < 0,y(t)y''(t) > 0$ for $ t \in [\alpha ,\infty )$ and $ {\lim _{t \to \infty }}y(t) = 0$, if (*) has an oscillatory solution. Further, sufficient conditions have been obtained so that (*) admits an oscillatory solution.

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Article copyright: © Copyright 1990 American Mathematical Society

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