Related papers: A note on linear differential equations with varia…
In this work, we consider a general time-periodic linear transport equation with integral source term. We prove the existence of a Floquet principal eigenvalue, namely a real number such that the equation rescaled by this number admits…
In this paper, a method to solve functionally commutative time- dependent linear homogeneous differential equation is discussed. We apply this technique to solve some dynamical quantum problems.
This paper provides a summary of the fractal calculus framework. It presents higher-order homogeneous and nonhomogeneous linear fractal differential equations with $\alpha$-order. Solutions for these equations with constant coefficients are…
A first order differential equation with a periodic operator coefficient acting in a pair of Hilbert spaces is considered. This setting models both elliptic equations with periodic coefficients in a cylinder and parabolic equations with…
In this article we study a class of generalised linear systems of difference equations with given non-consistent initial conditions and infinite many solutions. We take into consideration the case that the coefficients are square constant…
This article is devoted to the study of solutions of non-homogenous linear differential equations having entire coefficients. We get all non-trivial solutions of infinite order of equation $f^{(n)}+a_{n-1}(z)f^{(n-1)}+\ldots…
We consider first-order linear systems of ordinary differential equations with periodic coefficients. Supposing that right-hand sides of equations are not known and subjected to some quadratic restrictions, we obtain optimal, in certain…
This paper deals with reduction of non-homogeneous linear systems of first order operator equations with constant coefficients. An equivalent reduced system, consisting of higher order linear operator equations having only one variable and…
The article studies the reiterated homogenization of linear elliptic variational inequalities arising in problems with unilateral constrains. We assume that the coefficients of the equations satisfy and abstract hypothesis covering on each…
In this short note we are presenting a method of finding particular solutions of nonhomegeneous linear equations. This approach is different from methods of undetermined coefficients or variation of parameters presented in virtually every…
We analyze Floquet theory as it applies to the stability and instability of periodic traveling waves in Hamiltonian PDEs. Our investigation focuses on several examples of such PDEs, including the generalized KdV and BBM equations (third…
In this article, basing upon probabilistic methods, we discuss periodic homogenization of a class of weakly coupled systems of linear elliptic and parabolic partial differential equations. Under the assumption that the systems have rapidly…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
The classical Floquet theory allows to map a time-periodic system of linear differential equations into an autonomous one. By looking at it in a geometrical way, we extend the theory to a class of non-autonomous non-periodic equations. This…
We present a general formula for the particular solution of an inhomogeneous linear difference equation with variable coefficients. The answer is expressed as a weighted sum of fundamental solutions of the associated linear difference…
The Cauchy problem for fractional derivatives linear systems of ordinary differential equations with constant coefficients is considered, where at first the analytic expressions are given through the matrix exponent of its corresponding…
The solution to systems of moment differential equations of the form $z\partial_my=(zA+B)y$ are provided, for a matrix $B$ with general good spectrum. Existence and convergence of Floquet-type solutions is studied. A generalized definition…
In this short paper, a formula for the sequence defined by the nonhomogeneous linear difference equation with variable coefficients is presented. A connection with the homogeneous case is shown.
Nonequilibrium topological matter has been a fruitful topic of both theoretical and experimental interest. A great variety of exotic topological phases unavailable in static systems may emerge under nonequilibrium situations, often…
Fractional order differential and difference equations are used to model systems with memory. Variable order fractional equations are proposed to model systems where the memory changes in time. We investigate stability conditions for linear…