相关论文: A differential equation with state-dependent delay…
We consider abstract evolution equations with a nonlinear term depending on the state and on delayed states. We show that, if the $C_0$-semigroup describing the linear part of the model is exponentially stable, then the whole system retains…
We propose an alternative delayed population growth difference equation model based on a modification of the Beverton-Holt recurrence, assuming a delay only in the growth contribution that takes into account that those individuals that die…
An epidemic model with distributed time delay is derived to describe the dynamics of infectious diseases with varying immunity. It is shown that solutions are always positive, and the model has at most two steady states: disease-free and…
A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…
The purpose of this paper is to establish Picard-Lindel\"{o}f theorem for local uniqueness and existence results for first-order systems of nonlinear delay dynamic equations. In the linear case, we extend our results to global existence and…
We review $H^{1}$-well-posedness for initial value problems of ordinary differential equations with state-dependent right-hand side. We streamline known approaches to infer existence and uniqueness of solutions for small times given a…
In this paper, we first prove the stability equivalence between a linear autonomous and cooperative functional differential equation (FDE) and its associated autonomous and cooperative system without time delay. Then we present the theory…
The main objective of this work is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations (see's) and stochastic partial differential equations (spde's) near stationary solutions. Such…
We consider a linear scalar delay differential equation (DDE), consisting of two arbitrary distributed time delays. We formulate necessary conditions for stability of the trivial solution which are independent of the distributions. For the…
We consider a parabolic semilinear non-autonomous problem $(\tilde P)$ for a fractional time dependent operator $\mathcal{B}^{s,t}_\Omega$ with Wentzell-type boundary conditions in a possibly non-smooth domain $\Omega\subset\mathbb{R}^N$.…
Mathematical models of interacting populations are often constructed as systems of differential equations, which describe how populations change with time. Below we study one such model connected to the nonlinear dynamics of a system of…
The work considers a system of fractional order partial differential equations. The existence and uniqueness theorems for the classical solution of initial-boundary value problems are proved in two cases: 1) the right-hand side of the…
For a differential equation with a state-dependent delay we show that the associated solution manifold $X_f$ of codimnsion 1 in the space $C^1([-r,0],\mathbb {R})$ is an almost graph over a hyperplane, which implies that $X_f$ is…
A nonlinear time-delay model is proposed to describe the interaction dynamics between criminal and non-criminal populations, combining social influence mechanisms, saturation effects represented by a Holling type II functional response, and…
In this paper, we prove that a particular nondegenerate, nonlinear, autonomous parabolic partial differential equation with a nonlocal mass transfer admits the local existence of classical solutions. The equation was developed to…
Stochastic differential equations (SDEs) without global Lipschitz drift often demonstrate unusual phenomena. In this paper, we consider the following SDE on $\mathbb R^d$: \begin{align*} \mathrm{d} \mathbf{X}_t=\mathbf{b}(\mathbf{X}_t)…
By analogy with the theory of Backward Stochastic Differential Equations, we define Backward Stochastic Difference Equations on spaces related to discrete time, finite state processes. This paper considers these processes as constructions…
We study a mathematical model describing the dynamics of a pluripotent stem cell population involved in the blood production process in the bone marrow. This model is a differential equation with a time delay. The delay describes the cell…
In this paper, by using the spectral theory of functions and properties of evolution semigroups, we establish conditions on the existence, and uniqueness of asymptotic 1-periodic solutions to a class of abstract differential equations with…
We investigate state dependent delay differential equations with distributed memory, combining discrete state dependent delays and a convolution type memory operator. Under Lipschitz type assumptions on the delay, kernel, and nonlinear…