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Volume 10, Number 3, 2020, Pages 1118-1148                                                                DOI:10.11948/20190217
Approximate controllability of second-order semilinear evolution systems with state-dependent infinite delay
Xiaofeng Su,Xianlong Fu
Keywords:Second-order evolution equation, approximate controllability, cosine operator, fundamental solution, fractional power operator.
      In this article, we study the problem of approximate controllability for a class of semilinear second-order control systems with state-dependent delay. We establish some sufficient conditions for approximate controllability for this kind of systems by constructing fundamental solutions and using the resolvent condition and techniques on cosine family of linear operators. Particularly, theory of fractional power operators for cosine families is also applied to discuss the problem so that the obtained results can be applied to the systems involving derivatives of spatial variables.~To illustrate the applications of the obtained results, two examples are presented in the end.
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