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International Journal of Mathematical Research

February 2017, Volume 6, 2, pp 46-52

Period Monotonicity for Weight-Homogeneous Differential Systems

Khalil I.T. Al-Dosary


Hishyar Kh. Abdullah

Khalil I.T. Al-Dosary 1 ,

Hishyar Kh. Abdullah 1 
  1. College of Sciences, University of Sharjah, Sharjah, United Arab Emirates 1

Pages: 46-52

DOI: 10.18488/journal.24.2017.62.46.52

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Article History:

Received: 20 March, 2017
Revised: 30 May, 2017
Accepted: 23 June, 2017
Published: 13 July, 2017


In this article, integrability, center, and monotonicity of associated period function for  -quasi-homogeneous vector fields are investigated. We are concerned with family of vector field given by sum, finite or infinite number of quasi-homogeneous polynomials not necessarily to be sharing the same weights. The investigation is done by utilizing method of computing focal values. As an application of the result, a particular family of (p, q)-quasi-homogeneous vector field is studied to find conditions for center, monotonicity and consequently an explicit form for the associated period function.

Contribution/ Originality


Integrability, Centre, Period function, Quasi-homogeneous polynomial, Center-focus problem, Vector field.



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The authors would like to express their gratitude to the University of Sharjah for support

Competing Interests:

The authors declare that they have no competing interests.


Both authors contributed equally to the conception and design of the study.

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