Related papers: Oscillation results for first order neutral delay …

We give some sufficient conditions that ensure oscillations and nonoscillations for nonautonomous impulsive differential equations with piecewise constant arguments of generalized type. We cover several cases of differential equations with…

This work presents two simple criteria for determining the oscillatory nature of solutions to second-order differential equations with deviated arguments. These criteria extend the (Leighton-Wintner)-type criteria established by G.Q. Wang…

A sharp condition is provided to guarantee that the (nontrivial) solutions of a DDE of the form $\dot{x}(t)+F(t,x)=0$ $t\geq 0,$ (where $F(t,\cdot)$ is an odd-like causal operator) either oscillate, or converge monotonically to zero. The…

In this work, we shall consider the existence and uniqueness of stationary solutions to stochastic partial functional differential equations with additive noise in which a neutral type of delay is explicitly presented. We are especially…

We consider general nonlinear elliptic equations of the form \[ \operatorname{div}\, A(x,Du) = 0 \quad \text{in } \Omega, \] where $A:\Omega \times \mathbb R^n \to \mathbb R^n$ satisfies a quasi-isotropic $(p,q)$-growth condition, which is…

The Riccati equation method is used to establish three new oscillatory criteria for the second order linear ordinary differential equations in the marginal, sub extremal and extremal cases.We show that the first of these criteria implies…

Using the Riccati transformation techniques, we will extend some almost oscillation criteria for the second-order nonlinear neutral difference equation with quasidifferences $$\Delta\left(r_n\left(\Delta \left(x_n+c…

For a nonlinear equation with several variable delays $$ \dot{x}(t)=\sum_{k=1}^m f_k(t, x(h_1(t)),\dots,x(h_l(t)))-g(t,x(t)), $$ where the functions $f_k$ increase in some variables and decrease in the others, we obtain conditions when a…

For nonlinear wave equations with a potential term we prove pointwise space-time decay estimates and develop a perturbation theory for small initial data. We show that the perturbation series has a positive convergence radius by a method…

In this paper we study well-posedness and asymptotic stability for a class of nonlinear second-order evolution equations with intermittent delay damping. More precisely, a delay feedback and an undelayed one act alternately in time. We show…

This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…

A simple non-autonomous scalar differential equation with delay, exponential decay, nonlinear negative feedback and a periodic multiplicative coefficient is considered. It is shown that stable slowly oscillating periodic solutions with the…

In this study, we focus on the existence of a periodic solution for the neutral nonlinear dynamic systems with delay% \[ x^{\Delta}(t)=A(t)x(t)+Q^{\Delta}\left(t,x\left(\delta_{-}(s,t)\right) \right)…

The Riccati equation method and an approach of the use of unknown factors is used to establish oscillation, suboscillation and nonoscillation criteria for linear systems of ordinary differential equations. A necessary condition for Lyapunov…

We establish several delay-independent criteria for the existence and stability of positive periodic solutions of n-dimensional nonautonomous functional differential equation by several fixed point theorems. Examples from positive and…

In this paper we use the Riccati equation method with other ones to establish global solvability, stability and oscillation criteria for a class of two dimensional nonlinear systems of ordinary differential equations, which is a…

In this paper, we introduce the notion of boundary delay equations, establishing a unified framework for analyzing linear time-invariant systems with pure time-delayed boundary conditions. We establish mild sufficient conditions for the…

In this paper, we prove the existence and uniqueness of the solution for neutral stochastic differential delay equations with locally monotone coefficients by using numerical approximation. An example is provided to illustrate our theory.

The time-periodic scalar delay differential equation $\dot x(t)=\gamma f(t,x(t-1))$ is considered, which leads to a resonant bifurcation of the equilibrium at critical values of the parameter. Using Floquet theory, spectral projection and…

New explicit conditions of asymptotic and exponential stability are obtained for the scalar nonautonomous linear delay differential equation $$ \dot{x}(t)+\sum_{k=1}^m a_k(t)x(h_k(t))=0 $$ with measurable delays and coefficients. These…