Existence, uniqueness and continuous dependence for implicit semilinear functional differential equations Original Research Article

Theorems of existence, uniqueness and continuous dependence for the nonlinear functional differential equation d/dt(Au(t))+Bu(t)=f(t,ut) in a Banach space are proved. The unbounded operator A is, generally, degenerate. Abstract results are applied to nonlinear partial functional differential equations. In particular, a model of liquid filtration in fissured porous rocks is considered.