Abstract
We prove that some 2π-periodic generalized Abel equations of the form x′ = A(t)xn + B(t)xm + C(t)x, with n ≠ m and n, m < 2 have at most three limit cycles. The novelty of our result is that, in contrast with other results of the literature, our hypotheses allow the functions A,B, and C to change sign. Finally we study in more detail the Abel equation x′ = A(t)x3 + B(t)x2, where the functions A and B are trigonometric polynomials of degree one. © 2009 World Scientific Publishing Company.
Original language | English |
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Pages (from-to) | 3869-3876 |
Journal | International Journal of Bifurcation and Chaos |
Volume | 19 |
Issue number | 11 |
DOIs | |
Publication status | Published - 1 Jan 2009 |
Keywords
- Abel equation
- Limit cycle
- Periodic solution