VIABILITY FOR SEMILINEAR DIFFERENTIAL EQUATIONS OF RETARDED TYPE
VIABILITY FOR SEMILINEAR DIFFERENTIAL EQUATIONS OF RETARDED TYPE
Let X be a Banach space, <TEX>$A:D(A){\subset}X{\rightarrow}X$</TEX> the generator of a compact <TEX>$C_0-semigroup\;S(t):X{\rightarrow}X,\;t{\geq}0$</TEX>, D a locally closed subset in X, and <TEX>$f:(a,b){\times}C([-q,0];X){\rightarrow}X$</TEX> a function of Caratheodory type. The main result of this paper is that a necessary and sufficient condition in order that D be a viable domain of the …