Almost Periodic Differential Equations

Bounded and almost periodic solutions and evolution semigroups associated with nonautonomous functional differential equations

“…We then demonstrate an application of the obtained results to study the boundedness and almost periodicity of solutions to functional differential equations. As a result we get a sufficient condition for the existence of bounded and almost periodic solutions which is an extension to fully nonlinear functional differential equations of previous results by other authors (see [10,12,16,20,21] for related results and methods, [6,25] for more information on ordinary differential equations with almost periodic coefficients, and [8] for various conditions for almost periodicity of solutions of equations with infinite delay). In this paper, we put an emphasis on an application of evolution semigroup method to the study of boundedness and almost periodicity of solutions to nonlinear nonautonomous functional differential equations via nonlinear semigroup techniques.…”

Uniqueness and global exponential stability of almost periodic solution for Hematopoiesis model on time scales

“…If Γ = {R} and T = R , then Γ * = R, in this case, Definition 2.9 is equivalent to the definition of almost periodic function in [5]. If Γ = {Z} and T = Z , then Γ * = Z, in this case, Definition 2.9 is equivalent to the definition of almost periodic sequence in [3].…”

“…Almost periodicity is closer to the reality in biological systems [5,10]. However, to our knowledge, no papers deal with the existence and global exponential stability of unique almost periodic positive solution for the above model (1.1) on time scales.…”

A new composition theorem for $S^p$-weighted pseudo almost periodic functions and applications to semilinear differential equations

“…Definition 2.2 ( [27,28]). A function f ∈ C(R × Y, X) is said to be (Bohr) almost periodic in t ∈ R uniformly in y ∈ Y if for every ε > 0 and any compact K ⊂ Y there exists l(ε) > 0 such that every interval of length l(ε) contains a number τ with the property that f (t + τ, y) − f (t, y) < ε for each t ∈ R and y ∈ K. The collection of all such functions will be denoted by AP (R × Y, X).…”

“…By a standard argument, it is easy to prove that G b ∈ AP (L p ((0, 1), X)) (see, e.g., [27,Theorem 2.11]). To show that f (·, x(·)) ∈ W P AP S p (X), it is enough to show that…”