Abstract
In this paper, we first present an impulsive version of Filippov's Theorem for first-order semilinear functional differential inclusions of the form:
{(y' - Ay) is an element of F(t, y(t)) a.e. t is an element of J\{t(1),...,t(m)}, y(t(k)(+)) - y(t(k)(-)) = I-k(y(t(k)(-))) for k = 1,...,t(m)}, y(t) = phi(t) for t is an element of [-r, 0],
where J = [0, b], A is the infinitesimal generator of a C-0-semigroup on a separable Banach space E and F is a set-valued map. The functions I-k characterize the jump of the solutions at impulse Points t(k) (k = 1,...,m). Then the convexified problem is considered and a Filippov-Wazewski result is proved. Further to several existence results, the topological structure of solution sets - closeness and compactness - is also investigated. Some results from topological fixed point theory together with notions of measure on noncompactness are used. Finally, some geometric properties of solution sets, AR, R-delta-contractibility and acyclicity, corresponding to Aronszajn-Browder-Gupta type results, are obtained.