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Abstract
We study the number of limit cycles (isolated periodic solutions in
the set of all periodic solutions) for the generalized Abel equation
$x'=a(t)x^{n_a}+b(t)x^{n_b}+c(t)x^{n_c}+d(t)x$, where
$n_a > n_b > n_c > 1$, $a(t),b(t),c(t), d(t)$ are $2\pi$-periodic
continuous functions, and two of $a(t),b(t),c(t)$ have definite
sign.
We obtain examples with at least seven limit cycles, and some
sufficient conditions for the equation to have at most one or at
most two positive limit cycles.
Mathematics Subject Classification: Primary: 34C25; Secondary: 34A34, 37C27, 37G15.
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