Limit Cycles for a Class of Abel Equations
- 1 September 1990
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 21 (5), 1235-1244
- https://doi.org/10.1137/0521068
Abstract
The number of solutions of the Abel differential equation ${{dx(t)} /{dt}} = A(t)x(t)^3 + B(t)x(t)^2 + C(t)x(t)$ satisfying the condition $x(0) = x(1)$ is studied, under the hypothesis that either $A(t)$ or $B(t)$ does not change sign for $t in [0,1]$. The main result obtained is that there are either infinitely many or at most three such solutions. This result is also applied to control the maximum number of limit cycles for some planar polynomial vector fields with homogeneous nonlinearities.
Keywords
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