Existence and stability of almost periodic solutions of nonautonomous competitive systems with weak Allee effect and delays

A note on Arzela–Ascoli's lemma in almost periodic problems

“…In this paper, we give a counter example to show that the generalized Arzela-Ascoli's lemma is incorrect, and there is a gap in the proof of the existence of almost periodic solutions by using the coincidence degree method based on this lemma (cf. the related theorems in [14][15][16][17][18][19][20][21][22][23][24]). However, these theorems themselves may be right.…”

“…After this article was published, many scholars used the aforementioned method to obtain the L ‐compactness of mapping N and established the existence of almost periodic solutions for a large number of differential equation models by the continuation theorem. We can find some of these researches in . Moreover, Theorem was firstly proposed by Zeng and widely used to establish the existence of almost periodic solutions for differential equations .…”

Almost periodic solutions for a class of discrete systems with Allee-effect

“…We always apply the latter way to studying the almost periodic solutions for ecological systems, especially for discrete systems, in which we need first to study the persistence of the systems considered. In [23], [2], [22], applying the method of coincidence degree theory which is different from the previous results, the authors studied the almost periodic solutions for some classes of Lotka-Volterra systems. However, all of them only considered the continuous models.…”