Second-order impulsive differential systems with mixed and several delays

In this work, we present new necessary and sufficient conditions for the oscillation of a class of second-order neutral delay impulsive differential equations. Our oscillation results complement, simplify and improve recent results on oscillation theory of this type of nonlinear neutral impulsive differential equations that appear in the literature. An example is provided to illustrate the value of the main results.

Bolivia’s Double Pandemic

The November 2019 ouster of President Evo Morales, followed by the interim government’s harsh crackdown on his supporters, plunged Bolivia into a political crisis just as the COVID-19 pandemic arrived with devastating effect. The interim government’s haphazard response was marred by corruption scandals over procurement of medical supplies. After several delays, a general election was finally held in October 2019. Luis Arce, the presidential candidate of Morales’s Movement Toward Socialism, won decisively. But Morales’s subsequent return from exile signaled that the struggle over his legacy would continue.

Oscillatory and asymptotic properties of higher-order quasilinear neutral differential equations

<abstract><p>The objective of this paper is to study the oscillation criteria for odd-order neutral differential equations with several delays. We establish new oscillation criteria by using Riccati transformation. Our new criteria are interested in complementing and extending some results in the literature. An example is considered to illustrate our results.</p></abstract>

Delay-Dependent Stability Conditions for Non-autonomous Functional Differential Equations with Several Delays in a Banach Space

Let Bj (t) (j = 1,..., m) and B(t, τ) (t ≥ 0, 0 ≤ τ ≤ 1) be bounded variable operators in a Banach space. We consider the equation u ′ ( t ) = ∑ k = 1 m B k ( t ) u ( t - h k ( t ) ) + ∫ 0 1 B ( t , τ ) u ( t - h 0 ( τ ) ) d τ ( t ≥ 0 ) , u'\left( t \right) = \sum\limits_{k = 1}^m {{B_k}\left( t \right)u\left( {t - {h_k}\left( t \right)} \right)} + \int\limits_0^1 {B\left( {t,\tau } \right)u\left( {t - {h_0}\left( \tau \right)} \right)d\tau \,\,\,\,\left( {t \ge 0} \right),} where hk (t) (t ≥ 0; k = 1, ..., m) and h 0(τ) are continuous nonnegative bounded functions. Explicit delay-dependent exponential stability conditions for that equation are established. Applications to integro-differential equations with delay are also discussed

A Survey on Sharp Oscillation Conditions of Differential Equations with Several Delays

This paper deals with the oscillation of the first-order differential equation with several delay arguments x′t+∑i=1mpitxτit=0,t≥t0, where the functions pi,τi∈Ct0,∞,R+, for every i=1,2,…,m,τit≤t for t≥t0 and limt→∞τit=∞. In this paper, the state-of-the-art on the sharp oscillation conditions are presented. In particular, several sufficient oscillation conditions are presented and it is shown that, under additional hypotheses dealing with slowly varying at infinity functions, some of the “liminf” oscillation conditions can be essentially improved replacing “liminf” by “limsup”. The importance of the slowly varying hypothesis and the essential improvement of the sufficient oscillation conditions are illustrated by examples.

Oscillation for Super Linear/Linear Second Order Neutral Difference Equations with Variable Several Delays

This article, is concerned with finding sufficient conditions for the oscillation and non oscillation of the solutions of a second order neutral difference equation with multiple delays under the forward difference operator, which generalize and extend some existing results.This could be possible by extending an important lemma from the literature.