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Uniformly Lipschitz stability and asymptotic property of perturbed functional differential systems. (English) Zbl 1432.34092

Summary: This paper shows that the solutions to the perturbed functional differential system \[y'=f(t,y)+\int_{t_0}^t g(s,y(s),Ty(s))ds \] have uniformly Lipschitz stability and asymptotic property. To show these properties, we impose conditions on the perturbed part \(\int_{t_0}^t g(s,y(s),Ty(s))ds\) and the fundamental matrix of the unperturbed system \(y'=f(t,y)\).

MSC:

34K20 Stability theory of functional-differential equations
34D10 Perturbations of ordinary differential equations
45J05 Integro-ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
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References:

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