Positive almost periodic solutions for a delay logarithmic population model

Alzabut, Jehad; Stamov, Gani; Sermutlu, Emre

doi:10.1016/j.mcm.2010.07.029

Cited by 37 publications

(13 citation statements)

References 18 publications

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“…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.…”

Section: 1)ṅ (T) = N (T)[a(t) − B(t)n P (T − σ(T)) − C(t)n Q (T − τmentioning

confidence: 99%

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

Yang

2014

Appl Math

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Section: 1)ṅ (T) = N (T)[a(t) − B(t)n P (T − σ(T)) − C(t)n Q (T − τmentioning

confidence: 99%

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

Yang

2014

Appl Math

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“…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.…”

Section: Concluding Remarks and An Open Problemmentioning

confidence: 99%

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

Zhou

Shao

2016

Math Methods in App Sciences

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Communicated by Q. ChenThis paper is concerned with a generalized Arzela-Ascoli's lemma, which has been extensively applied in almost periodic problems by the continuation theorem of degree theory. We give a counter example to show that this lemma is incorrect, and there is a gap in the proof of some existing literature, where the addressed generalized Arzela-Ascoli's lemma was used. Moreover, we make some final comments and introduce an open problem.

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“…Remark 8. Since [14,15] only obtain the existence and local exponential stability of positive almost periodic solutions for delay logarithmic population model (1), one can observe that all the results in this literature and the references therein can not be applicable to prove the existence and global exponential stability of positive almost periodic solution for (51). This implies that the results of this paper are essentially new.…”

Section: An Examplementioning

confidence: 99%

“…Hence, it is of great importance to consider the dynamical behaviors of logarithmic population model with almost periodically varying coefficient. Recently, by utilizing the continuation theorem and contraction mapping principle, some criteria have been established to prove the existence and local exponential stability of positive almost periodic solutions for delay logarithmic population model and its generalized modification in the literature; see [13][14][15][16][17]. However, to the best of our knowledge, there is no literature considering the existence and global exponential stability of positive almost periodic solutions problem for delay logarithmic population model.…”

Section: Introductionmentioning

confidence: 99%