Opuscula Math. 40, no. 3 (2020), 341-360
https://doi.org/10.7494/OpMath.2020.40.3.341

 
Opuscula Mathematica

Existence of periodic positive solutions to nonlinear Lotka-Volterra competition systems

Mimia Benhadri
Tomás Caraballo
Halim Zeghdoudi

Abstract. 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, On positive periodic solution of Lotka-Volterra competition systems with deviating arguments, 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.

Keywords: Krasnoselskii's fixed point theorem, positive periodic solutions, Lotka-Volterra competition systems, variable delays.

Mathematics Subject Classification: 34K20, 34K13, 92B20.

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  • Tomás Caraballo (corresponding author)
  • ORCID iD https://orcid.org/0000-0003-4697-898X
  • Departamento de Ecuaciones Difererenciales y Análisis Numérico, Universidad de Sevilla, c/ Tarfia s/n, 41012 - Sevilla, Spain
  • Communicated by Josef Diblík.
  • Received: 2018-12-23.
  • Revised: 2020-02-23.
  • Accepted: 2020-02-29.
  • Published online: 2020-04-04.
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Cite this article as:
Mimia Benhadri, Tomás Caraballo, Halim Zeghdoudi, Existence of periodic positive solutions to nonlinear Lotka-Volterra competition systems, Opuscula Math. 40, no. 3 (2020), 341-360, https://doi.org/10.7494/OpMath.2020.40.3.341

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