Electron. J. Diff. Equ., Vol. 2011 (2011), No. 124, pp. 1-6.

Non-existence of limit cycles via inverse integrating factors

Leonardo Laura-Guarachi, Osvaldo Osuna, Gabriel Villasenor-Aguilar

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.

Submitted September 1, 2011. Published September 27, 2011.
Math Subject Classifications: 34C05, 34C07, 34C25.
Key Words: Algebraic set; integrating factors; inverse integrating factors; limit cycles.

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Leonardo Laura-Guarachi
Instituto de Física y Matemáticas
Universidad Michoacana, Edif. C-3, Cd. Universitaria
C.P. 58040. Morelia, Mich., México
email: leonardo@ifm.umich.mx
Osvaldo Osuna
Instituto de Física y Matemáticas
Universidad Michoacana, Edif. C-3, Cd. Universitaria
C.P. 58040. Morelia, Mich., México
email: osvaldo@ifm.umich.mx
Gabriel Villaseñor-Aguilar
Instituto de Física y Matemáticas
Universidad Michoacana, Edif. C-3, Cd. Universitaria
C.P. 58040. Morelia, Mich., México
email: gabriel@ifm.umich.mx

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