Total stability in abstract functional differential equations with infinite delay.(English)Zbl 0973.34063

Summary: For functional-differential equations with infinite delay in a Banach space, an equivalent relationship between the BC-total stability and the $$\rho$$-total stability is investigated, and a result due to S. Murakami and T. Yoshizawa on functional-differential equations in a finite-dimensional space [Tohoku Math. J., II. Ser. 44, No. 1, 45-57 (1992; Zbl 0793.34056)] is extended to the one on functional-differential equations in a general Banach space.

MSC:

 34K20 Stability theory of functional-differential equations 34K30 Functional-differential equations in abstract spaces

Zbl 0793.34056
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