LIMITING EQUATIONS OF INTEGRODIFFERENTIAL EQUATIONS IN BANACH-SPACE

The ''limiting equation'' results for integrodifferential equations in finite dimensional space are extended to equations x'(t) = A[x(t) + integral(0)(1)F(t - s)x(s) ds] + f(t), t greater than or equal to 0, (a) and y'(t) = A[y(t) + integral(-x)(1) F(t - s)y(s) ds] + g(t). t is an element of R, (b) in reflexive Banach space in a weak sense when A is a closed and densely defined operator and F(t) is a bounded operator t greater than or equal to 0. The results are applied to study the periodic solutions of Eq. (b) on R. An application to a heat equation is also given. (C) 1994 Academic Press, Inc.