Almost periodic linear differential equations with non-separated solutions

Almost periodic linear differential equations with non-separated solutions

A celebrated result by Favard states that, for certain almost periodic linear differential systems, the existence of a bounded solution implies the existence of an almost periodic solution. A key assumption in this result is the separation among bounded solutions. Here we prove a theorem of anti-Favard type: if there are bounded solutions which are non-separated (in a strong sense) sometimes al...

ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR CERTAIN NON-LINEAR DIFFERENTIAL EQUATIONS

Here we consider some non-autonomous ordinary differential equations of order n and present some results and theorems on the existence of periodic solutions for them, which are sufficient conditions, section 1. Also we include generalizations of these results to vector differential equations and examinations of some practical examples by numerical simulation, section 2. For some special cases t...

Almost Periodic Solutions of Second Order Nonlinear Differential Equations with Almost Periodic Forcing

Existence and stability of almost-periodic solutions of quasi-linear differential equations with deviating argument

3(dx,t____~ =A( t ) x ( t )+ f ( t , x ( t ) ) , x ( t r l ( t ) ) , . . . , x ( t f k (t)), (1) dt such that the associated homogeneous linear system satisfies exponential dichotomy and deviations of the argument axe not restricted by any sign assumption. The exponential stability of the solution when the system is with delay argument is considered. (~) 2004 Elsevier Ltd. All rights reserved. ...

Square-mean Almost Periodic Solutions Nonautonomous Stochastic Differential Equations

This paper concerns the square-mean almost periodic solutions to a class of nonautonomous stochastic differential equations on a separable real Hilbert space. Using the so-called ‘Acquistapace-Terreni’ conditions, we establish the existence and uniqueness of a square-mean almost periodic mild solution to those nonautonomous stochastic differential equations.