## Topological Methods in Nonlinear Analysis

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

#### Abstract

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.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 49, Number 1 (2017), 273-298.

Dates
First available in Project Euclid: 11 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1491876030

Digital Object Identifier
doi:10.12775/TMNA.2016.076

Mathematical Reviews number (MathSciNet)
MR3635646

Zentralblatt MATH identifier
06773125

#### Citation

Xiao, Jian-Zhong; Wang, Zhi-Yong; Liu, Juan. Hausdorff product measures and $C^1$-solution sets of abstract semilinear functional differential inclusions. Topol. Methods Nonlinear Anal. 49 (2017), no. 1, 273--298. doi:10.12775/TMNA.2016.076. https://projecteuclid.org/euclid.tmna/1491876030

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