  A wide class of non-autonomous nonlinear parabolic partial differential
equations with delay is studied. We allow in our investigations different types
of delays such as constant, time-dependent, state-dependent (both discrete and
distributed) to be presented simultaneously. The main difficulties arise due to
the presence of discrete state-dependent delays since the nonlinear delay term
is not Lipschitz on the space of continuous functions. We find conditions for
the local existence, uniqueness and study the invariance principle.
