Oscillatory Properties of Certain Nonlinear Matrix Differential Systems of Second Order

Oscillatory Properties of Certain Nonlinear Matrix Differential Systems of Second Order

where Y, Z, Kix) and G(x) are « x n matrices and each of Kix) and G(x) is a symmetric matrix of continuous functions on a z% x < oo. By a solution of (b) we mean a pair of n x n matrices {T(x),Z(x)} such that each of the elements of Y and Z is a differentiable function and such that {Y,Z} satisfies the initial condition and satisfies the matrix differential system almost everywhere on a S! x < ...

On Oscillatory Nonlinear Second Order Neutral Delay Differential Equations

In this work, we investigate the oscillation criteria for second order neutral delay differential equations of the form (r(t)[y(t)+ p(t)y(δ (t))]′)′ +q(t)G(y(τ(t))) = 0 and (r(t)[[y(t)+ p(t)y(δ (t))]′]α )′ +q(t)(yβ (τ(t))) = 0, where α and β are the ratio of odd positive integers. Mathematics subject classification (2010): 34C10, 34C15.

Oscillation Criteria for Nonlinear Second Order Matrix Differential Equations

Abstract. The object of this paper is to present sufficient conditions for the oscillation of certain solutions of the second order, nonlinear matrix differential equation. The oscillation criteria obtained here improve the recent results of the author and E. C. Tomastik. The methods employed in the paper extend a technique introduced by H. C. Howard and for the special linear version of the no...

ON TE EXISTENCE OF PERIODIC SOLUTION FOR CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS

Nonlinear oscillation of certain third-order neutral differential equation with distributed delay

The authors obtain necessary and sufficient conditions for the existence of oscillatory solutions with a specified asymptotic behavior of solutions to a nonlinear neutral differential equation with distributed delay of third order. We give new theorems which ensure that every solution to be either oscillatory or converges to zero asymptotically. Examples dwelling upon the importance of applicab...