Bounded Solutions of Perturbed Volterra lntegrodifferential Systems
نویسنده
چکیده
More recently (P) has been studied under the weaker assumption that (L) is admissible with respect to certain pairs of spaces. The author [2] proved under such admissibility assumptions that locally the set of bounded solutions of (P) is homeomorphic to the set of bounded solutions of (L), provided p satisfies a Lipschitz-type condition in X. Other authors [I, 6J have obtained similar and related results using a different approach for a restricted class of systems (A(S) = A, B(t, S) = B(t s)). Our purpose here is to extend our previous results in [2] to a broader class of perturbations; the expense of this generalization is less structure for the set of bounded solutions of (P) as related to the corresponding set for (L). This set will no longer necessarily be locally homeomorphic to that of (L), but nevertheless will be “at least as large;” we make this precise by using the notation of locally nonempty partitions with respect to an index set as defined below. Our main results appear in Theorem 1.
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