On the weakly almost periodic solutions of certain abstract differential equations

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...

On Periodic Solutions of Abstract Differential Equations

On the Bohr Transform of Almost-periodic Solutions for Some Differential Equations in Abstract Spaces

We consider abstract differential equations of the form u′(t) = Au(t)+f(t) or u′′(t)=Au(t)+f(t) in Banach spaces X, where f(·), R→X is almost-periodic, while A is a linear operator, (A)⊂X →X. If the solution u(·) is likewise almost-periodic, R→X, we establish connections between their Bohr-transforms, û(λ) and f̂ (λ). 2000 Mathematics Subject Classification. 34C27, 34G10.

On Almost Periodic Differential Equations

The notion of an invariant set has been widely exploited in the theory of autonomous ordinary differential equations. The purpose of this announcement is to give a natural and useful generalization of invariant sets to almost periodic systems. The proofs and several applications and extensions of our results will appear elsewhere. We consider systems of n first order, almost periodic, ordinary ...

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...