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Approximate controllability of time-dependent impulsive semilinear retarded differential equations with infinite delay and nonlocal conditions

Abstract:

Here we study the approximate controllability of time dependent impulsive retarded semilinear differential equations with infinite delay and nonlocal conditions, where some ideas are taking from a previous works for this kind of systems with impulses, nonlocal conditions and finite delay, this is done using a techniques evading fixed point theorems used by A.E. Bashirov et al. In this case we have to impose some conditions on the nonlinear term depending of the last time impulse tp, so that we can prove the approximate controllability of this system by living the impulses behind on a fixed solution curve in a small interval of time, and from this position, we are able to reach a ball of center the final state and radius ɛ > 0 small enough, at time τ, by assuming that the associated linear control system is exactly controllable on any interval [t0, τ], 0 < t0 < τ.