Related papers: A note on linear differential equations with varia…
Consider a differential system of the form $$ x'=F_0(t,x)+\sum_{i=1}^k \varepsilon^i F_i(t,x)+\varepsilon^{k+1} R(t,x,\varepsilon), $$ where $F_i:\mathbb{S}^1 \times D \to \mathbb{R}^m$ and $R:\mathbb{S}^1 \times D \times…
We establish a Floquet theorem for a first-order system of differential equations $u'=ru$ where $r$ is an $n\times n$-matrix whose entries are periodic distributions of order $0$. Then we investigate, when $n=1$ and $n=2$, the spectral…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
Characterizing time-periodic Hamiltonians is pivotal for validating and controlling driven quantum platforms, yet prevailing and unadjusted reconstruction methods demand dense time-domain sampling and heavy post-processing. We introduce a…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…
The linear nonhomogeneous fractional difference system with constant coefficients is introduced. An explicit solution to the system is acquired by proposing a newly discrete retarded perturbation of the nabla Mittag-Leffer-type function…
Time-periodic dynamical systems occur commonly both in nature and as engineered systems. Large-scale linear time-periodic dynamical systems, for example, may arise through linearization of a nonlinear system about a given periodic solution…
We study linear systems of ordinary differential equations of an arbitrary order on a finite interval with the most general (generic) inhomogeneous boundary conditions in Sobolev spaces. We investigate the character of solvability of…
We develop an eigenvalue-based approach for the stability assessment and stabilization of linear systems with multiple delays and periodic coefficient matrices. Delays and period are assumed commensurate numbers, such that the Floquet…
We present an analytical approach to deal with nonlinear delay differential equations close to instabilities of time periodic reference states. To this end we start with approximately determining such reference states by extending the…
In this article, we study about the solutions of second order linear differential equations by considering several conditions on the coefficients of homogenous linear differential equation and its associated non-homogenous linear…
We dedicate this paper to the topological analysis of subwavelength solutions in Floquet metamaterials. This work should be considered as a basis for further investigation on whether topological properties of the bulk materials are linked…
In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential…
Consider the resolvent problem associated with the linearized viscous flow around a rotating body. Within a setting of classical Sobolev spaces, this problem is not well posed on the whole imaginary axis. Therefore, a framework of…
This paper is concerned with homogenization of systems of linear elasticity with rapidly oscillating periodic coefficients. We establish sharp convergence rates in $L^2$ for the mixed boundary value problems with bounded measurable…
Using the new periodicity concept based on shifts, we construct a unified Floquet theory for homogeneous and nonhomogeneous hybrid periodic systems on domains having continuous, discrete or hybrid structure. New periodicity concept based on…
This paper investigates the stability of switched linear systems whose switching signal is modeled as a stochastic process called a regenerative process. We show that the mean stability of such a switched system is characterized by the…
This paper exhibits a very simple formula for a particular solution of a linear ordinary differential equation with constant real coefficients, P(d/dt)x = f, f a function given by a linear combination of polynomials, trigonometrical and…
In this paper we study in a Hilbert space a homogeneous linear second order difference equation with nonconstant and noncommuting operator coefficients. We build its exact resolutive formula consisting in the explicit non-iterative…