Asymptotic Behavior of Solutions of Nonlinear Neutral Delay Forced Impulsive Differential Equations with Positive and Negative Coefficients

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 analysis of nonlinear hybrid delayed systems described by impulsive fuzzy differential equations

In this paper we introduce some stability criteria of nonlinear hybrid systems with time delay described by impulsive hybrid fuzzy system of differential equations. Firstly, a comparison principle for fuzzy differential system based on a notion of upper quasi-monotone nondecreasing is presented. Here, for stability analysis of fuzzy dynamical systems, vector Lyapunov-like functions are defined....

Asymptotic behavior of impulsive neutral delay differential equations with positive and negative coefficients of Euler form

Oscillatory and Asymptotic Behavior of Fourth Order Nonlinear Neutral Delay Differential Equations with Positive and Negative Coefficients

In this paper, Oscillatory and asymptotic behaviour of solutions of a class of nonlinear fourth order neutral differential equations with positive and negative coefficients of the form (H) (r(t)(y(t) + p(t)y(t− τ))′′)′′ + q(t)G(y(t− α)) − h(t)H(y(t− β)) = 0 and (NH) (r(t)(y(t) + p(t)y(t− τ))′′)′′ + q(t)G(y(t− α)) − h(t)H(y(t− β)) = f(t) are studied under the assumption ∫ ∞

Asymptotic Behavior of Solutions of Impulsive Differential Equations with Positive and Negative Coefficients

This paper is concerned with the impulsive delay differential equations with positive and negative coefficients  x′(t) + p(t)x(t− τ)− q(t)x(t− σ) = 0, t ≥ t0, t 6= tk, x(tk) = bkx(tk ) + (1− bk) (∫ tk tk−τ p(s+ τ)x(s)ds − ∫ tk tk−σ q(s+ σ)x(s)ds ) , k = 1, 2, 3, · · · . Sufficient conditions are obtained for every solution of the above equation tends to a constant as t→∞.