  In this paper, we analyze a semilinear damped second order evolution equation
with time-dependent time delay and time-dependent delay feedback coefficient.
The nonlinear term satisfies a local Lipschitz continuity assumption. Under
appropriate conditions, we prove well-posedness and exponential stability of
our model for small initial data. Our arguments combine a Lyapunov functional
approach with some continuity arguments. Moreover, as an application of our
abstract results, the damped wave equation with a source term and delay
feedback is analyzed.
