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Upper bounds for the number of limit cycles of some planar polynomial differential systems

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  • We give an effective method for controlling the maximum number of limit cycles of some planar polynomial systems. It is based on a suitable choice of a Dulac function and the application of the well-known Bendixson-Dulac Criterion for multiple connected regions. The key point is a new approach to control the sign of the functions involved in the criterion. The method is applied to several examples.
    Mathematics Subject Classification: Primary: 34C05, 34C07; Secondary: 37C27.


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