Weak almost periodic solutions of differential equations

Almost-Periodic Weak Solutions of Second-Order Neutral Delay-Differential Equations with Piecewise Constant Argument

Differential equations with piecewise constant argument, which were firstly considered by Cooke and Wiener 1 , and Shah and Wiener 2 , usually describe hybrid dynamical systems a combination of continuous and discrete and so combine properties of both differential and difference equations. Over the years, great attention has been paid to the study of the existence of almost-periodic-type soluti...

Ergodicity and Asymptotically Almost Periodic Solutions of Some Differential Equations

Using ergodicity of functions, we prove the existence and uniqueness of (asymptotically) almost periodic solution for some nonlinear differential equations. As a consequence, we generalize a Massera’s result. A counterexample is given to show that the ergodic condition cannot be dropped. 2000 Mathematics Subject Classification. Primary 34C27, 43A60, 37Axx, 28Dxx.

Asymptotic equivalence of differential equations and asymptotically almost periodic solutions

In this paper we establish asymptotic (biasymptotic) equivalence between spaces of solutions of a given linear homogeneous system and a perturbed system. The perturbations are of either linear or weakly linear characters. Existence of a homeomorphism between subspaces of almost periodic and asymptotically (biasymptotically) almost periodic solutions is also obtained.

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

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.