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

Hino, Yoshiyuki; Murakami, Satoru

Electron. J. Qual. Theory Differ. Equ. 2000, Suppl., 9 p. (2000).

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

Keywords:

functional-differential equations; infinite delay; BC-total stability; \(\rho\)-total stability

Citations:

Zbl 0793.34056