By means of the exponential dichotomy method and the properties of the weighted pseudo almost periodic functions, sufficient conditions are obtained for the existence of weighted pseudo almost periodic solutions of functional differential equations with finite delay.

A sequence {un}n∈ω in abstract additively-written Abelian group G is called a T -sequence if there is a Hausdorff group topology on G relative to which limn un = 0. We say that a subgroupH of an infinite compact Abelian groupX is T -characterized if there is a T -sequence u = {un} in the dual group of X , such that H = {x ∈ X : (un, x) → 1}. We show that a closed subgroupH ofX is T -characteriz...

We study strong solutions u : R → X, a Banach space X, of the nth-order evolution equation u(n) −Au(n−1) = f , an infinitesimal generator of a strongly continuous group A : D(A) ⊆ X → X, and a given forcing term f : R → X. It is shown that if X is reflexive, u and u(n−1) are Stepanov-bounded, and f is Stepanov almost periodic, then u and all derivatives u′, . . . ,u(n−1) are strongly almost per...

We consider the attractors for the two-dimensional nonautonomous Navier-Stokes equations in some unbounded domain Ω with nonhomogeneous boundary conditions. We apply the so-called uniformly ω-limit compact approach to nonhomogeneous Navier-Stokes equation as well as a method to verify it. Assuming f ∈ Lloc 0, T ;L2 Ω , which is translation compact and φ ∈ C1 b R ;H2 R1 × {±L} asymptotically alm...

We study convergence of positive solutions for almost periodic reaction diffusion equations of Fisher or Kolmogorov type. It is proved that under suitable conditions every positive solution is asymptotically almost periodic. Moreover, all positive almost periodic solutions are harmonic and uniformly stable, and if one of them is spatially homogeneous, then so are others. The existence of an alm...