Approximate controllability for abstract semilinear impulsive functional differential inclusions based on Hausdorff product measures.(English)Zbl 1414.34061

Summary: 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.

MSC:

 34K35 Control problems for functional-differential equations 34K45 Functional-differential equations with impulses 34K09 Functional-differential inclusions 34K30 Functional-differential equations in abstract spaces 93B05 Controllability
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