Abstract
Using a monotonicity property specific to this case, we give a general property of the stability pattern of successive periodic solutions of the first-order scalar differential equation u′ = f(t, u). We also give an optimal smallness condition in order for the quasi-autonomous equation u′+g(u) = f(t) where g ∈ C1(ℝ) and f : ℝ → ℝ is almost periodic to have exactly N almost periodic solutions on the line assuming that we have exactly N equilibria ci and g′(ci) ≠ 0 for all i.
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