Journal of Applied Mathematics and Stochastic Analysis
Volume 7 (1994), Issue 4, Pages 537-544
doi:10.1155/S1048953394000419
Abstract
We prove the existence of a continuous selection of the multivalued map
φ→Φ(φ) which is the set of all mild solutions of the evolution inclusion
x(t)∈Ax(t)+F(t,x(t))+∫0th(t−s)g(x(s))dsx(0)=φ.
Here F is a multivalued map, Lipschitzian with respect to x, and A is the
infinitesimal generator of a C0-semigroup.