%% R.E. Showalter: Chapter 8
\chapter{Suggested Readings}
\leftline{\bf Chapter I}
\indent This material is covered in almost every text on functional analysis.
We mention specifically references
\cite{hellwig}, \cite{horvath}, \cite{yosida}.
\medskip
\leftline{\bf Chapter II}
Our definition of distribution in Section 1 is inadequate for many purposes.
For the standard results see any one of
\cite{carroll}, \cite{hormander}, \cite{horvath}.
For additional information on Sobolev spaces we refer to
\cite{adams}, \cite{aubin}, \cite{friedman}, \cite{lionsMag}, \cite{necas}.
\medskip
\leftline{\bf Chapter III}
Linear elliptic boundary value problems are discussed in the references
\cite{agmon}, \cite{aubin}, \cite{friedman},
\cite{lionsMag}, \cite{mizohata}, \cite{necas}
by methods closely related to ours.
See \cite{hellwig}, \cite{hormander}, \cite{treves}, \cite{yosida}
for other approaches.
For basic work on nonlinear problems we refer to
\cite{browder}, \cite{carroll}, \cite{lionsQM}, \cite{strauss}.
\medskip
\leftline{\bf Chapter IV}
We have only touched on the theory of semigroups; see
\cite{butzer}, \cite{friedman}, \cite{goldstein}, \cite{hille},
\cite{ladas}, \cite{yosida} for additional material.
Refer to \cite{carroll}, \cite{friedman}, \cite{ladySU}, \cite{lionsDO}
for hyperbolic problems and
\cite{carroll}, \cite{jeffrey}, \cite{lax}, \cite{mizohata}
for hyperbolic systems.
Corresponding results for nonlinear problems are given in
\cite{brezis}, \cite{browder}, \cite{carroll},
\cite{lionsQM}, \cite{martin}, \cite{strauss}, \cite{yosida}.
\newpage
\leftline{\bf Chapter V and VI}
The standard reference for implicit evolution equations is \cite{carrshow}.
Also see \cite{lionsDO} and \cite{lionsQM}, \cite{strauss} for related linear
and nonlinear results, respectively.
\medskip
\leftline{\bf Chapter VII}
For extensions and applications of the basic material of Section~2 see
\cite{carroll}, \cite{cea}, \cite{ekeland}, \cite{rocka}, \cite{vainberg}.
Applications and theory of variational inequalities are presented in
\cite{duvaut}, \cite{fichera}, \cite{lionsQM};
their numerical approximation is given in \cite{glow}.
See \cite{lionsPDE} for additional topics in optimal control.
The theory of approximation of partial differential equations is given in
references \cite{aubin}, \cite{ciarlet}, \cite{odenreddy}, \cite{schultz},
\cite{strang}; also see \cite{cea}, \cite{daniel}.
\medskip
\leftline{\bf Additional Topics}
We have painfully rejected the temptation to pursue many interesting topics;
each of them deserves attention.
A few of these topics are improperly posed problems
\cite{carasso}, \cite{payne},
function-theoretic methods \cite{colton},
bifurcation \cite{dickey},
fundamental solutions \cite{hormander}, \cite{treves},
scattering theory \cite{lax},
the transposition method \cite{lionsMag},
non-autonomous evolution equations \cite{browder}, \cite{carroll},
\cite{carrshow}, \cite{friedman}, \cite{ladas}, \cite{lionsDO},
\cite{martin}, \cite{yosida}, and
singular problems \cite{carrshow}.
Classical treatments of partial differential equations of elliptic and
hyperbolic type are given in the treatise \cite{courant}
and the canonical parabolic equation is discussed in \cite{widder}.
These topics are similarly presented in \cite{tychonov}
together with derivations of many initial and boundary value problems
and their applications.