Abstract
In this paper, we consider a second-order abstract viscoelastic equation in Hilbert spaces with time-varying delay and a very general class of memory kernel functions. Under some suitable conditions and by introducing a suitable Lyapunov functional, we state and prove explicit and general stability results of the energy. We give also some applications to illustrate our results. This work generalizes the previous results without time delay term to those with time-varying delay.
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