Displaying similar documents to “On oscillation and asymptotic property of a class of third order differential equations”

On the oscillation of a class of linear homogeneous third order differential equations

N. Parhi, P. Das (1998)

Archivum Mathematicum

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In this paper we have considered completely the equation y ' ' ' + a ( t ) y ' ' + b ( t ) y ' + c ( t ) y = 0 , ( * ) where a ∈ C 2 ( [ σ , ∞ ) , R ) , b ∈ C 1 ( [ σ , ∞ ) , R ) , c ∈ C ( [ σ , ∞ ) , R ) and σ ∈ R such that a ( t ) ≤ 0 , b ( t ) ≤ 0 and c ( t ) ≤ 0 . It has been shown that the set of all oscillatory solutions of (*) forms a two-dimensional subspace of the solution space of (*) provided that (*) has an oscillatory solution. This answers a question raised by S. Ahmad and A.  C. Lazer earlier.

Global monotonicity and oscillation for second order differential equation

Miroslav Bartušek, Mariella Cecchi, Zuzana Došlá, Mauro Marini (2005)

Czechoslovak Mathematical Journal

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Oscillatory properties of the second order nonlinear equation ( r ( t ) x ' ) ' + q ( t ) f ( x ) = 0 are investigated. In particular, criteria for the existence of at least one oscillatory solution and for the global monotonicity properties of nonoscillatory solutions are established. The possible coexistence of oscillatory and nonoscillatory solutions is studied too.