Necessary and sufficient conditions for oscillations of neutral differential equations

Necessary and sufficient conditions for oscillations of first order neutral delay difference equations with constant coefficients

In this paper, we establish the necessary and sufficient conditions for oscillation of the following first order neutral delay difference equation ∆[x(n) + px(n− τ)] + qx(n− σ) = 0, n ≥ n0, (∗) where τ and σ are positive integers, p 6= 0 is a real number and q is a positive real number. We proved that every solution of (∗) oscillates if and only if its characteristic equation (λ− 1)(1 + pλ−τ ) ...

Necessary and Sufficient Conditions for Oscillations of Neutral Delay Difference Equations with Several Coefficients

Necessary and Sufficient Conditions for Oscillation of Neutral Delay Differential Equations

In this article, we concerned with oscillation of the neutral delay differential equation [x(t) − px(t − τ)]′ + qx(t − σ) = 0 with constant coefficients. By constructing several suitable auxiliary functions, we obtained some necessary and sufficient conditions for oscillation of all the solutions of the aforementioned equation for the cases 0 < p < 1 and p > 1.

Necessary and sufficient conditions for oscillation of first order neutral delay difference equations

In this paper, we obtained some necessary and sufficient conditions for oscillation of all the solutions of the first order neutral delay difference equation with constant coefficients of the form ∆[x(n)− px(n− τ)] + qx(n− σ) = 0, n ≥ n0 (∗) by constructing several suitable auxiliary functions. Some examples are also given to illustrate our results.

Oscillations for Neutral Functional Differential Equations

We will consider a class of neutral functional differential equations. Some infinite integral conditions for the oscillation of all solutions are derived. Our results extend and improve some of the previous results in the literature.