%% 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.