Non-existence of limit cycles via inverse integrating factors

Abstract

It is known that if a planar differential systems has an inverse integrating factor, then all the limit cycles contained in the domain of definition of the inverse integrating factor are contained in the zero set of this function. Using this fact we give some criteria to rule out the existence of limit cycles. We also present some applications and examples that illustrate our results.

Keywords

• Algebraic set
• integrating factors
• inverse integrating factors
• limit cycles