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Browsing by Subject "variable delays"

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    Item type:Article, Access status: Open Access ,
    Existence of periodic positive solutions to nonlinear Lotka-Volterra competition systems
    (Wydawnictwa AGH, 2020) Benhadri, Mimia; Caraballo, Tomás; Zeghdoudi, Halim
    We investigate the existence of positive periodic solutions of a nonlinear Lotka-Volterra competition system with deviating arguments. The main tool we use to obtain our result is the Krasnoselskii fixed point theorem. In particular, this paper improves important and interesting work [X.H. Tang, X. Zhou, <i>On positive periodic solution of Lotka-Volterra competition systems with deviating arguments</i>, Proc. Amer. Math. Soc. 134 (2006), 2967-2974]. Moreover, as an application, we also exhibit some special cases of the system, which have been studied extensively in the literature.
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Fixed points and stability in neutral nonlinear differential equations with variable delays
    (2012) Ardjouni, Abdelouaheb; Djoudi, Ahcene
    By means of Krasnoselskii’s fixed point theorem we obtain boundedness and stability results of a neutral nonlinear differential equation with variable delays. A stability theorem with a necessary and sufficient condition is given. The results obtained here extend and improve the work of C.H. Jin and J.W. Luo [Nonlinear Anal. 68 (2008), 3307–3315], and also those of T.A. Burton [Fixed Point Theory 4 (2003), 15-32; Dynam. Systems Appl. 11 (2002), 499–519] and B. Zhang [Nonlinear Anal. 63 (2005), e233–e242]. In the end we provide an example to illustrate our claim.