相关论文: Compact almost automorphic dynamics of non-autonom…

We study almost automorphic solutions of the discrete delayed neutral dynamic system% \[ x(t+1)=A(t)x(t)+\Delta Q(t,x(t-g(t)))+G(t,x(t),x(t-g(t))) \] by means of a fixed point theorem due to Krasnoselskii. Using discrete variant of…

In this article we introduce a class of discontinuous almost automorphic functions which appears naturally in the study of almost automorphic solutions of differential equations with piecewise constant argument. Their fundamental properties…

We establish existence and uniqueness of remotely almost periodic (RAP) solutions for nonlinear ordinary differential systems $x' = A(t)x + f(t,x) + g_{\nu}(t,x).$ Assuming that the linear equation $x' = A(t)x$ admits an exponential…

In this paper, we first propose a new concept of almost periodic time scales, a new definition of almost automorphic functions on almost periodic time scales, and study some their basic properties. Then we prove a result ensuring the…

Existence of almost automorphic solutions for abstract delayed differential equations is established. Using ergodicity, exponential dichotomy and Bi-almost automorphicity on the homogeneous part, sufficient conditions for the existence and…

In this article we completely characterise constant length substitution shifts which have an almost automorphic factor, or which have a bijective substitution factor. Our approach is algebraic: we study these dynamical properties in terms…

Using properties of asymptotically almost periodic solutions we prove existence theorem for piece-wise continuous almost periodic solutions of differential equations with delay and impulses. We apply these results to study almost periodic…

In this work we give a criterion to have an exponential dichotomy over all $\mathbb{R}$ for delayed systems $x'(t)=L(t)x_t$, where $L_{\pm}=\lim_{t\to\pm\infty}L(t)$, and the systems $x'(t)=L_{\pm}x_t$ are autonomous and hyperbolic. The…

Let $(X,G)$ be a minimal equicontinuous dynamical system, where $X$ is a compact metric space and $G$ some topological group acting on $X$. Under very mild assumptions, we show that the class of regular almost automorphic extensions of…

We study the discretization of a linear evolution partial differential equation when its Green function is known. We provide error estimates both for the spatial approximation and for the time stepping approximation. We show that, in fact,…

We study long-time dynamics of a class of abstract second order in time evolution equations in a Hilbert space with the damping term depending both on displacement and velocity. This damping represents the nonlinear strong dissipation…

A discrete countable group G is matricially stable if the finite dimensional approximate unitary representations of G are perturbable to genuine representations in the point-norm topology. For large classes of groups G, we show that…

For a H\'{e}non map $H$ in $\mathbb{C}^2$, we characterize the polynomial automorphisms of $\mathbb{C}^2$ which keep any fixed level set of the Green function of $H$ completely invariant. The interior of any non-zero sublevel set of the…

The exponential ordering is exploited in the context of non-auto\-no\-mous delay systems, inducing monotone skew-product semiflows under less restrictive conditions than usual. Some dynamical concepts linked to the order, such as…

In this paper, we prove that for a large class of growth-decay-fragmentation problems the solution semigroup is analytic and compact and thus has the Asynchronous Exponential Growth property.

We consider existence and stability of an almost periodic solution of the quasilinear system of differential equations with piecewise constant argument of generalized type. The associated linear homogeneous system satisfies exponential…

The main results of this article provide asymptotics at infinity of the Green's functions near and at the spectral gap edges for "generic" periodic second-order elliptic operators on noncompact Riemannian co-compact coverings with abelian…

Let \(\mathcal{G}\) be a non-empty subset of the Euclidean space \(\mathbb{R}^m\) (\(m \geq 1\)). This work is dedicated to further exploring the properties of \(\mathcal{G}\)-multi-almost automorphic functions defined on \(\mathbb{R}^m\)…

We are concerned with the almost automorphic solutions to the second-order elliptic differential equations of type $\ddot u(s) + 2 B \dot u(s) + A u(s) = f(s) (\ast),$ where $A, B$ are densely defined closed linear operators acting in a…

We investigate singular perturbation problems caused by small delays in the view of pseudo-exponential dichotomy. For a general linear non-autonomous retarded differential equation with small delay, previous works established the existence…