International Journal of Mathematical Research 2311-7427 2306-2223 10.18488/journal.24.2017.62.46.52 International Journal of Mathematical Research Period Monotonicity for Weight-Homogeneous Differential Systems International Journal of Mathematical Research International Journal of Mathematical Research 02-2017 2017 02-2017 02-2017 6 2 46 52 20 Mar 2017 23 Jun 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.<br>