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Global stability for a class of delay differential equations. (English) Zbl 1064.34061
The paper is concerned with the study of the behavior of solutions of the delay differential equation \[ {\dot x}(t) = \alpha f(x(t-1)), x(t) = x^0(t) \quad\text{for }t \in [-1, 0] \] where \(\alpha \geq 0\) and \(f\) is a continuously differentiable unimodal mapping with \(f(0)=f(1)=0\). The author gives sufficient conditions for the nonnegativity of solutions of the equation and for the global stability of the solutions.

34K20 Stability theory of functional-differential equations
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