Incomplete second order linear differential equations in Banach
spaces as well as first order equations have become a classical
part of functional analysis. This monograph is an attempt to
present a unified systematic theory of second order equations y"
(t) + Ay' (t) + By (t) = 0 including well-posedness of the Cauchy
problem as well as the Dirichlet and Neumann problems. Exhaustive
yet clear answers to all posed questions are given. Special
emphasis is placed on new surprising effects arising for complete
second order equations which do not take place for first order and
incomplete second order equations. For this purpose, some new
results in the spectral theory of pairs of operators and the
boundary behavior of integral transforms have been developed. The
book serves as a self-contained introductory course and a reference
book on this subject for undergraduate and post- graduate students
and research mathematicians in analysis. Moreover, users will
welcome having a comprehensive study of the equations at hand, and
it gives insight into the theory of complete second order linear
differential equations in a general context - a theory which is far
from being fully understood.
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