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Topological Methods in Nonlinear Analysis

Approximate controllability for abstract semilinear impulsive functional differential inclusions based on Hausdorff product measures
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Approximate controllability for abstract semilinear impulsive functional differential inclusions based on Hausdorff product measures

Authors

  • Jian-Zhong Xiao
  • Xing-Hua Zhu

Keywords

Approximate controllability, impulsive system, second order semilinear differential inclusion, Cosine family of operators, fixed point for multivalued mapping

Abstract

A second order semilinear impulsive functional differential inclusion in a separable Hilbert space is considered. Without imposing hypotheses of the compactness on the cosine families of operators, some sufficient conditions of approximate controllability are formulated in the case where the multivalued nonlinearity of the inclusion is a completely continuous map dominated by a function. By the use of resolvents of controllability Gramian operators and developing appropriate computing techniques for the Hausdorff product measures of noncompactness, the results of approximate controllability for position and velocity are derived. An example is also given to illustrate the application of the obtained results.

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Published

2018-11-24

How to Cite

1.
XIAO, Jian-Zhong and ZHU, Xing-Hua. Approximate controllability for abstract semilinear impulsive functional differential inclusions based on Hausdorff product measures. Topological Methods in Nonlinear Analysis. Online. 24 November 2018. Vol. 52, no. 2, pp. 353 - 372. [Accessed 4 July 2025].
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