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Approximate controllability of neutral functional differential systems with state-dependent delay

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Abstract

This paper deals with the approximate controllability of semilinear neutral functional differential systems with state-dependent delay. The fractional power theory and α-norm are used to discuss the problem so that the obtained results can apply to the systems involving derivatives of spatial variables. By methods of functional analysis and semigroup theory, sufficient conditions of approximate controllability are formulated and proved. Finally, an example is provided to illustrate the applications of the obtained results.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai, 200241, China

    Xianlong Fu & Jialin Zhang

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  1. Xianlong Fu
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  2. Jialin Zhang
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Correspondence to Xianlong Fu.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11171110, 11371087), the Science and Technology Commission of Shanghai Municipality (No. 13dz2260400) and the Shanghai Leading Academic Discipline Project (No. B407).

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Fu, X., Zhang, J. Approximate controllability of neutral functional differential systems with state-dependent delay. Chin. Ann. Math. Ser. B 37, 291–308 (2016). https://doi.org/10.1007/s11401-016-0934-z

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  • DOI: https://doi.org/10.1007/s11401-016-0934-z

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