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Fixed points and stability in linear neutral differential equations with variable delays. (English) Zbl 1216.34069

The equation
\[ x'(t) = -\sum^N_{j=1}b_j(t)x(t-\tau_j(t)) +\sum^N_{j=1}c_j(t)x'(t-\tau(t)) \]
is considered. Under suitable assumptions, a necessary and sufficient condition is found for the zero solution to be asymptotically stable. This improves and generalises some available results.

MSC:

34K20 Stability theory of functional-differential equations
34K40 Neutral functional-differential equations
34K06 Linear functional-differential equations
34K21 Stationary solutions of functional-differential equations
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References:

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