Almost periodic solutions of evolution equations

New Spectral Criteria for Almost Periodic Solutions of Evolution Equations

We present a general spectral decomposition technique for bounded solutions to inhomogeneous linear periodic evolution equations of the form _ x = A(t)x+f(t) (), with f having precompact range, which will be then applied to nd new spectral criteria for the existence of almost periodic solutions with speciic spectral properties in the resonnant case where e isp(f) may intersect the spectrum of t...

Almost Periodic and Periodic Solutions of Difference Equations

I t is easy to see that for every point (y, N) in WXI there is a solution (n) of (1) that satisfies <1>(N) =y. This solution is defined and unique on some set N^nKN*» where N<» is maximal. (That is, either iV» = °o or ^ i V ^ — l) (£W.) The solution may or may not be continuable for nƒ> rc)> 0^w<iV o o(^ , / ) , be the soluti...

Periodic solutions for evolution equations ∗

We study the existence and uniqueness of periodic solutions for evolution equations. First we analyze the one-dimensional case. Then for arbitrary dimensions (finite or not), we consider linear symmetric operators. We also prove the same results for non-linear sub-differential operators A = ∂φ where φ is convex.

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

Asymptotically Almost Periodic and Almost Periodic Solutions for a Class of Partial Integrodifferential Equations

In this note, we establish the existence of asymptotically almost periodic and almost periodic solutions for a class of partial integrodifferential equations.