Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 124, pp. 1-6.
Title: Non-existence of limit cycles via inverse integrating factors
Authors: Leonardo Laura-Guarachi (Univ. Michoacana, Morelia, Mexico)
Osvaldo Osuna (Univ. Michoacana, Morelia, Mexico)
Gabriel Villasenor-Aguilar (Univ. Michoacana, Morelia, Mexico)
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.