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Oscillation Theorems for Second Order Sublinear Ordinary Differential Equations

Elabbasy, E. (1997)

Serdica Mathematical Journal

Oscillation criteria are given for the second order sublinear non-autonomous differential equation. (r(t) (x)x′(t))′ + q(t)g(x(t)) = (t). These criteria extends and improves earlier oscillation criteria of Kamenev, Kura, Philos and Wong. Oscillation criteria are also given for second order sublinear damped non-autonomous differential equations.

Oscillations of higher order differential equations of neutral type

N. Parhi (2000)

Czechoslovak Mathematical Journal

In this paper, sufficient conditions have been obtained for oscillation of solutions of a class of n th order linear neutral delay-differential equations. Some of these results have been used to study oscillatory behaviour of solutions of a class of boundary value problems for neutral hyperbolic partial differential equations.

Oscillatory and asymptotic behaviour of solutions of advanced functional equations

Jozef Džurina (1993)

Archivum Mathematicum

In this paper we compare the asymptotic behaviour of the advanced functional equation L n u ( t ) - F ( t , u [ g ( t ) ] ) = 0 with the asymptotic behaviour of the set of ordinary functional equations α i u ( t ) - F ( t , u ( t ) ) = 0 . On the basis of this comparison principle the sufficient conditions for property (B) of equation (*) are deduced.

Oscillatory and non oscillatory criteria for the systems of two linear first order two by two dimensional matrix ordinary differential equations

Gevorg Avagovich Grigorian (2018)

Archivum Mathematicum

The Riccati equation method is used for study the oscillatory and non oscillatory behavior of solutions of systems of two first order linear two by two dimensional matrix differential equations. An integral and an interval oscillatory criteria are obtained. Two non oscillatory criteria are obtained as well. On an example, one of the obtained oscillatory criteria is compared with some well known results.

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