相关论文: Oscillation results for first order neutral delay …

We consider the prototype equation x'(t) = f(x(t-1)) for delayed negative feedback. We review known results on uniqueness and nonuniqueness of slowly oscillating periodic solutions, and present some new results and examples.

A class of periodic differential $n$-dimensional systems with patch structure with (possibly infinite) delay and nonlinear impulses is considered. These systems incorporate very general nonlinearities and impulses whose signs may vary.…

An understanding of the oscillations of differentially rotating systems is key to many areas of astrophysics. It is of particular relevance to the emission of gravitational waves from oscillating neutron stars, which are expected to possess…

We discuss the occurrence of positive solutions which decay to 0 as $| x|\to+\infty$ to the differential equation $\Delta u+f(x,u)+g(| x|)x\cdot\nabla u=0$, $| x|>R>0$, $x\in\mathbb{R}^{n}$, where $n\geq 3$, $g$ is nonnegative valued and…

Exponential stability and solution estimates are investigated for a delay system $$ \dot{x}(t) - A(t)\dot{x}(g(t))=\sum_{k=1}^m B_k(t)x(h_k(t)) $$ of a neutral type, where $A$ and $B_k$ are $n\times n$ bounded matrix functions, and $g, h_k$…

In this paper, we determine a concrete interval of positive parameters $\lambda$, for which we prove the existence of infinitely many homoclinic solutions for a discrete problem $-\Delta \left( a(k)\phi _{p}(\Delta u(k-1))\right)…

We use the Riccati equation method with other ones to establish new oscillation and interval oscillation criteria for linear matrix Hamiltonian systems. We investigate the oscillation problem for linear matrix Hamiltonian systems in a new…

In this paper, we present sufficient conditions for asymptotic stability and exponential stability of a class of impulsive neutral differential equations with discrete and distributed delays. Our approaches are based on the method using…

Analysis of the systems involving delay is a popular topic among applied scientists. In the present work, we analyze the generalized equation $D^{\alpha} x(t) = g\left(x(t-\tau_1), x(t-\tau_2)\right)$ involving two delays viz. $\tau_1\geq…

We present a condition for delay-independent stability of a class of nonlinear positive systems. This result applies to systems that are not necessarily monotone and extends recent work on cooperative nonlinear systems.

We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…

Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…

In this note we unify the results of A.C. Lazer and P.O. Frederickson [3], A.C. Lazer [6], A.C. Lazer and D.E. Leach [7], J.M. Alonso and R. Ortega [1], and P. Korman and Y. Li [4] on periodic oscillations and unbounded solutions of…

The purpose of this paper is to give an Osgood's criterion for solutions of semilinear stochastic differential equations of the form $X_{t}=\xi +\int_{0}^{t}b(s,X_{s})ds+\int_{0}^{t}\sigma (s)X_{s}dW_{s},\ t\geq 0$. Here, $b$ is a…

For $1<p<\infty$, we consider the following problem $$ -\Delta_p u=f(u),\quad u>0\text{ in }\Omega,\quad\partial_\nu u=0\text{ on }\partial\Omega, $$ where $\Omega\subset\mathbb R^N$ is either a ball or an annulus. The nonlinearity $f$ is…

In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…

In this paper we consider the linear ordinary equation of the second order $$ L x(t)\equiv \ddot{x}(t) +a(t)\dot{x}(t)+b(t)x(t)=f(t), \eqno{(1)} $$ and the corresponding homogeneous equation $$ \ddot{x}(t) +a(t)\dot{x}(t)+b(t)x(t)=0.…

We prove expansion of positivity and reduction of the oscillation results to the local weak solutions to a doubly nonlinear anisotropic class of parabolic differential equations with bounded and measurable coefficients, whose prototype is…

The effects of delayed feedback terms on nonlinear oscillators has been extensively studied, and have important applications in many areas of science and engineering. We study a particular class of second-order delay-differential equations…

We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…