Pseudo compact almost automorphic solutions for a family of delayed population model of Nicholson type

Pseudo compact almost automorphic solutions to a family of non-monotone delayed differential equations

“…. By the same arguments as in the proof of [7,Lemma 4], it is easy to get that F 2 ∈ P AP 0 (R, R). Now it remains to prove that F 3 ∈ P AP 0 (R, R).…”

“…(ii) In [7], the nonlinear term F i (λ i (t)u) = ue −λi(t)u in Nicholson model and F i (λ i (t)u) = e −λi(t)u in Lasota-Wazewska model satisfy the following assumption:…”

Almost Periodic Functions and Their Applications: A Survey of Results and Perspectives

“…Almost periodicity in mathematical biology: there exist numerous research articles concerning almost periodic-and almost automorphic-type solutions for various classes of ordinary and partial differential equations appearing in mathematical biology (see, e.g., the recent article [157] by Abbas, Dama, Pinto, and Sepulveda, monograph [5], and the references quoted therein). In this section, we will present the main details of the investigation [158] carried out by Ding, Liang, and Xiao and the investigation [159] carried out by Zhang, Yang, and Wang.…”

Hartman and Nirenberg type results for systems of delay differential equations under $ (\omega,Q) $-periodic conditions

“…In particular, if 1 is not an eigenvalue of the (invertible) orthogonal matrix Q, then a Hartman type condition [11] is obtained when V (x) = |x| 2 . This is the idea of our first existence theorem for (1), that shall be proven in Section 2 by means of the Poincaré translation operator. It is remarked that, in contrast with [23], the assumption that Q is an orthogonal matrix is here relaxed.…”

“…In this paper, we continue with this study. Specifically, for a fixed invertible matrix Q ∈ R n×n , we shall consider the affine or (ω, Q)-periodic problem for the system X (t) = F (t, X(t), X(t − τ )) (1) where F : R × R 2n → R n is a continuous function satisfying…”