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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 $\tau>0$, $p(t)\ge 0$, $\delta(t)$ 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:
34K14Almost and pseudo-periodic solutions of functional differential equations
34K06Linear functional-differential equations
34K05General theory of functional-differential equations
34K20Stability theory of functional-differential equations
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References:
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