Topics in Abstract Differential Equations: v. 1

This monograph presents results concerning differential equations in abstract (Banach and Hilbert) spaces. The actual treatment of the subject is based on several of the author's papers and includes the following list of topics: the abstract Cauchy problem for differential equations of singular type; uniqueness of bounded solutions on the real line; the abstract Cauchy problem for regular differential equations; almost-periodic solutions; periodic solutions; asymptotically almost-periodic and almost-automorphic solutions; a local existence result for a non-homogeneous Sobolev equation; and regularity and regularization of weak and ultraweak solutions.