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Almost periodic solutions of Lasota-Wazewska-type delay differential equation. (English) Zbl 0936.34058

The authors consider nonautonomous delay differential equations of Lasota-Wazewska-type: \[ x'(t)=-\delta(t)x(t)+p(t)f(x(t-\tau)), \tag{1} \] where \(\tau>0\), \(p(t)\geq 0\), \(\delta(t)\) are continuous almost-periodic functions, \(f\) is a decreasing positive \(C^1\)-function. Sufficient conditions for the existence of a globally attractive almost-periodic solution to (1) is obtained. Conditions on the uniform asymptotical stability for some associated linear equations \[ x'(t)=-\delta(t)x(t)+p(t)x(t-\tau) \] are discussed. Examples for the obtained general theorems are provided.

MSC:

34K14 Almost and pseudo-almost periodic solutions to functional-differential equations
34K06 Linear functional-differential equations
34K05 General theory of functional-differential equations
34K20 Stability theory of functional-differential equations
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