Necessary and sufficient conditions for oscillation of neutral equation

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.

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.

Conditions for Oscillation of a Neutral Differential Equation

Necessary and Sufficient Conditions for the Oscillation of Differential Equations Involving Distributed Arguments

In this article, we establish necessary and sufficient conditions for the oscillation of both bounded and unbounded solutions of the differential equation

Necessary and Sufficient Conditions for Copositive Tensors

In this paper, it is proved that a symmetric tensor is (strictly) copositive if and only if each of its principal subtensors has no (non-positive) negative H++-eigenvalue. Necessary and sufficient conditions for (strict) copositivity of a symmetric tensor are also given in terms of Z++-eigenvalues of the principal sub-tensors of that tensor. This presents a method for testing (strict) copositiv...