Hausdorff product measures and $C^1$-solution sets of abstract semilinear functional differential inclusions

Jian-Zhong Xiao, Zhi-Yong Wang, Juan Liu



A second order semilinear neutral functional differential inclusion with nonlocal conditions and multivalued impulse characteristics in a separable Banach space is considered. By developing appropriate computing techniques for the Hausdorff product measures of noncompactness, the topological structure of $C^1$-solution sets is established; and some interesting discussion is offered when the multivalued nonlinearity of the inclusion is a weakly upper semicontinuous map satisfying a condition expressed in terms of the Hausdorff measure.


Impulsive functional inclusion; cosine family of operators; fixed point for multivalued map; measure of noncompactness

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