Positive Periodic Solutions of Coupled Singular Rayleigh Systems

Kong Fanchao ^[1] ; Liang, Feng ^[1] ; Nieto, Juan J ^[2]
1. [1] Anhui Normal University
  
  Anhui Normal University
  
  China
2. [2] Universidade de Santiago de Compostela
  
  Universidade de Santiago de Compostela
  
  Santiago de Compostela, España
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 3, 2020
Idioma: inglés
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Resumen
- This paper mainly aims to investigate the positive periodic solutions for coupled singular Rayleigh systems. In order to establish the coupled structure, the basic framework of graph theory is employed. By means of Lyapunov method, inequality techniques and a classical consequence of Mawhin’s continuation theorem, some sufficient criterion for the positive periodic solutions has been provided. After that, taken the effects of the delays into account and without imposing more conditions, we further study the positive periodic solutions for a kind of coupled singular Rayleigh system with delays. Here not only the structure is more general than the existing works but the conditions imposed are concise. Consequently, compared with the previous results on the singular systems and coupled systems, the results we established are more generalized and some previous ones can been complemented and improved. Finally, the effectiveness of the established results are validated via an numerical example.