  In this note we develop a framework which allows to prove an existence result
for non-linear evolution problems involving time-dependent, pseudo-monotone
operators. This abstract existence result is applicable to a large class of
concrete problems where the standard theorem on evolutionary pseudo-monotone
operators is not applicable. To this end we introduce the notion of Bochner
pseudo-monotonicity, and Bochner coercivity, which are appropriate extensions
of the concepts of pseudo-monotonicity and coercivity to the evolutionary
setting. Moreover, we give sufficient conditions for these new notions, which
are easily and widely applicable.
