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Stability for a class of differential equations with nonconstant delay. (English) Zbl 1269.34079

Summary: Stability is investigated for the following differential equations with nonconstant delay \[ x'(t) = g(t)F(x(t)) - p(t)f(x(t - \tau(t))), \] where \(p : [0, +\infty) \to [0, +\infty)\), \(q : [0, +\infty) \to\mathbb{R}\), \(\tau : [0, +\infty) \to [0, r)\), and \(F\) and \(f : \mathbb{R} \to \mathbb{R}\) with \(xf(x) > 0\) for \(x \neq 0\) and \(|x| \leq a\) (\(a\) is a positive constant) are continuous functions. A criterion is given for the zero solution of this delay equation being uniformly stable and asymptotically stable.

MSC:

34K20 Stability theory of functional-differential equations
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