Related papers: Levitan Almost Periodic Solutions of Linear Differ…

In this paper we present a formal analysis of the long-time asymptotics of a particular class of solutions of the Boltzmann equation, known as homoenergetic solutions, which have the form $f\left( x,v,t\right)=g\left( v-L\left( t\right)…

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 prove the existence of quasi-periodic solutions for wave equations with a multiplicative potential on T^d, d \geq 1, and finitely differentiable nonlinearities, quasi-periodically forced in time. The only external parameter is the length…

The existence of sufficiently many finite order meromorphic solutions of a differential equation, or difference equation, or differential-difference equation, appears to be a good indicator of integrability. In this paper, we investigate…

We study the reducibility of a Linear Schr\"odinger equation subject to a small unbounded almost-periodic perturbation which is analytic in time and space. Under appropriate assumptions on the smallness, analiticity and on the frequency of…

For a class of polynomial non-autonomous differential equations of degree n, we use phase plane analysis to show that each equation in this class has n periodic solutions. The result implies that certain rigid two-dimensional systems have…

This paper is devoted to the study of periodic (in time) solutions to an one-dimensional semilinear wave equation with $x$-dependent coefficients under various homogeneous boundary conditions. Such a model arises from the forced vibrations…

In this paper we prove the existence and the stability of small-amplitude quasi-periodic solutions with Sobolev regularity, for the 1-dimensional forced Kirchoff equation with periodic boundary conditions. This is the first KAM result for a…

We address two pressing questions in the theory of the Korteweg--de Vries (KdV) equation. First, we show the uniqueness of solutions to KdV that are merely bounded, without any further decay, regularity, periodicity, or almost periodicity…

We show that a type of linear superposition principle works for several nonlinear differential equations. Using this approach, we find periodic solutions of the Kadomtsev-Petviashvili (KP) equation, the nonlinear Schrodinger (NLS) equation,…

The issue of inheriting periodicity of an exact solution of a dynamic system by a difference scheme is considered. It is shown that some difference schemes (midpoint scheme, Kahan scheme) in some special cases provide approximate solutions…

The aim of this paper is studying the problem of existence of asymptotically periodic solutions of the scalar differential equation $x'=f(t,x),$ where $f:\mathbb R\times \mathbb R\to \mathbb R$ is a continuous asymptotically $\tau$-periodic…

We approximate a chain recurrent dynamical system by periodic dynamical systems. This is similar to the well known Bohr theorem on approximation of almost periodic functions by periodic functions.

We consider 1D completely resonant nonlinear wave equations of the type v_{tt}-v_{xx}=-v^3+O(v^4) with spatial periodic boundary conditions. We prove the existence of a new type of quasi-periodic small amplitude solutions with two…

A simple non-autonomous scalar differential equation with delay, exponential decay, nonlinear negative feedback and a periodic multiplicative coefficient is considered. It is shown that stable slowly oscillating periodic solutions with the…

In this paper we provide a version of the Floquet's theorem to be applied to any second order difference equations with quasi-periodic coefficients. To do this we extend to second order linear difference equations with quasi-periodic…

In this manuscript, we deal with some particular type of homogeneous first order linear systems with variable coefficients, in which we provide qualitative properties of the solution. When the coefficients of the indeterminate functions are…

The paper examines the existence of pseudo almost periodic solutions to some classes of partial hyperbolic evolution equations. Namely, sufficient conditions for the existence and uniqueness of pseudo almost periodic solutions to those…

In this work we study the existence of periodic and asymptotically periodic solutions of a system of nonlinear Volterra difference equations with infinite delay. By means of fixed point theory, we furnish conditions that guarantee the…

We study existence and uniqueness of bounded solutions to a fractional sublinear elliptic equation with a variable coefficient, in the whole space. Existence is investigated in connection to a certain fractional linear equation, whereas the…