Higher-order degenerate Cauchy problems in locally convex spaces

We establish a criterion for the C-well-posedness of higher order degenerate Cauchy problems (DCPn) in a sequentially complete locally convex space by introducing a C-propagation family {P(t)}t≥0 for (DCPn). This result is applied then to a class of (DCP2) whose coefficient operators are differential operators on various function spaces with Fréchet topologies and two C-well-posedness Theorems are obtained.