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Fixed points and stability of a nonconvolution equation. (English) Zbl 1050.34110

This paper deals with the asymptotic stability of the zero solution of the equation
\[ x'(t)=-\int_{t-r}^{t}a(t,s)g(x(s))\,ds, \]
where \(r>0\), and \(a:[0,\infty)\times [-r,\infty)\to \mathbb R\) is continuous.

MSC:

34K20 Stability theory of functional-differential equations
47H10 Fixed-point theorems
45J05 Integro-ordinary differential equations
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