Topological Methods in Nonlinear Analysis
- Topol. Methods Nonlinear Anal.
- Volume 52, Number 2 (2018), 353-372.
Approximate controllability for abstract semilinear impulsive functional differential inclusions based on Hausdorff product measures
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.
Topol. Methods Nonlinear Anal., Volume 52, Number 2 (2018), 353-372.
First available in Project Euclid: 25 November 2018
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Xiao, Jian-Zhong; Zhu, Xing-Hua. Approximate controllability for abstract semilinear impulsive functional differential inclusions based on Hausdorff product measures. Topol. Methods Nonlinear Anal. 52 (2018), no. 2, 353--372. doi:10.12775/TMNA.2018.030. https://projecteuclid.org/euclid.tmna/1543114845