Sufficient conditions for controllability of semilinear functional integrodifferential systems in a Banach space are established. The results are obtained by using the Schaefer fixed-point theorem.
We consider the second order initial value problem in a Hilbert space, which is a singular perturbation of a first order initial value problem. The difference of the solution and its singular limit is estimated in terms of the small parameter The coefficients are commuting self-adjoint operators and the estimates hold also for the semilinear problem.
In this paper we consider evolution inclusions of subdifferential type. First, we prove a convergence result and a continuous dependence proposition for abstract Cauchy problem of the form u' ∈ -∂⁻f(u) + G(u), u(0) = x₀, where ∂⁻f is the Fréchet subdifferential of a function f defined on an open subset Ω of a real separable Hilbert space H, taking its values in IR ∪ {+∞}, and G is a multifunction from C([0,T],Ω) into the nonempty subsets of L²([0,T],H). We obtain analogous results for the multivalued...