Solvability of Degenerate Semilinear Parabolic Functional Differential Equations

We obtain local and global theorems on the existence and uniqueness of a solution of the semilinear functional differential equation \(\frac{d}{{dt}}\left[ {Au\left( t \right)} \right] + Bu\left( t \right) = f\left( {t,u_t } \right)\) in a Banach space with a parabolic pencil of operators λA + B, where the operator A can be noninvertible. Abstract results are applied to partial functional differential equations.