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Fixed points and stability in differential equations with variable delays. (English) Zbl 1159.34348

Summary: We consider a linear scalar differential equation with variable delays and give conditions to ensure that the zero solution is asymptotically stable by means of fixed point theory. These conditions do not require the boundedness of delays, nor do they ask for a fixed sign on the coefficient functions. An asymptotic stability theorem with a necessary and sufficient condition is proved.

MSC:

34K20 Stability theory of functional-differential equations
34K40 Neutral functional-differential equations
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