Oscillation Properties of a Class of Nonlinear Differential Equations of Neutral Type

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...

Stability of two classes of improved backward Euler methods for stochastic delay differential equations of neutral type

This paper examines stability analysis of two classes of improved backward Euler methods, namely split-step $(theta, lambda)$-backward Euler (SSBE) and semi-implicit $(theta,lambda)$-Euler (SIE) methods, for nonlinear neutral stochastic delay differential equations (NSDDEs). It is proved that the SSBE method with $theta, lambdain(0,1]$ can recover the exponential mean-square stability with some...

Oscillation Criteria for Even-order Nonlinear Neutral Differential Equations of Mixed Type (communicated By

This paper deals with oscillation criteria for even order nonlinear neutral mixed type differential equations of the form

Oscillation Properties of a Class of Neutral Differential Equations with Positive and Negative Coefficients

In this paper, oscillatory and asymptotic property of solutions of a class of nonlinear neutral delay differential equations of the form (E) d dt (r(t) d dt (y(t) + p(t)y(t− τ))) + f1(t)G1(y(t− σ1))− f2(t)G2(y(t− σ2)) = g(t) and d dt (r(t) d dt (y(t) + p(t)y(t− τ))) + f1(t)G1(y(t− σ1))− f2(t)G2(y(t− σ2)) = 0 are studied under the assumptions ∞ ∫ 0 dt r(t) <∞ and ∞ ∫

EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR NEUTRAL DIFFERANCE EQUATIONS WITH VARIABLE DELAY