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\Large \textbf{Preface}
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The tradition of the Czechoslovak EQUADIFF conferences dates back to 1962
when EQUADIFF 1 was organized in Prague. In addition to 160 local
participants  it  was  attended by 75 foreign mathematicians. Subsequent
conferences held in Bratislava (1966, 1981, 1993), Brno (1972, 1985) and
Prague (1977, 1989) turned EQUADIFF into the world's oldest series of
comprehensive  conferences  on differential equations. EQUADIFF is
at  present one of the most important and biggest conferences of this kind.

The  Conference  on Differential Equations and Their Applications
EQUA\-DIFF  9 was held in Brno, August 25--29, 1997. It was organized by
the  \href{http://www.muni.cz}{Masaryk}  \href{http://www.muni.cz}{University},  
Brno in cooperation with \href{http://www.math.cas.cz}{Mathematical Institute} 
of the Academy of Sciences, \href{http://www.vutbr.cz}{Technical University} Brno,
Union  of  Czech  Mathematicians and Physicists, Union of Slovak
Mathematicians   and   Physicists  and  other  Czech  scientific
institutions  with  support  of  the  \href{http://elib.zib-berlin.de/IMU}{International Mathematical
Union}.  EQUADIFF 9 was  attended  by  269 participants  from  32
countries  and more than 50 accompanying persons and other guests.

EQUADIFF 9 was prepared by the Organizing Committee presided by
F.~Neuman, chairman, J.~Vosmansk\'y, executive secretary, 
Z.~Do\v{s}l\'a, head of the Equadiff Office, and other members J.~Dibl\'\i k,
O.~Do\v{s}l\'y, J.~Franc\r{u}, J.~Kalas, J.~Kuben, Z.~Posp\'\i\v{s}il and J.~\v{S}im\v{s}a.

The scientific program was prepared by the Scientific Committee.
It consisted of the following Czech and Slovak mathematicians:
P.~Dr\'abek, J.~Haslinger, J.~Jaro\v{s}, J.~Ka\v{c}ur, J.~Milota, J.~Ne\v{c}as, 
F.~Neuman (chairman) and \dag\,M.~Zl\'amal. The
invited speakers have been proposed by the international Honorary
and Advisory Board, consisted of R.\,P.~Agarwal, I.~Babu\v{s}ka, 
V.\,E.~Barbu, P.~Brunovsk\'y, W.\,N.~Everitt, A.~Friedman, J.\,K.~Hale, 
W.~J\"ager, I.\,T.~Kiguradze, K.~Kirsch\-g\"as\-sner, J.~Kurzweil (honorary
chairman), V.~Lakshmikantham, I.~Marek, J.~Maw\-hin, J.~Ne\v{c}as,
M.~R\'ab, K.~Rektorys, M.~\v{S}vec, R.~Temam, W.\,L.~Wendland and 
\dag\,M.~Zl\'amal.

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The scientific program comprised 8 plenary lectures and 34 main
lectures in the following sections:
\begin{enumerate}
\item Ordinary  differential equations,
\item Partial differential equations,
\item Numerical methods and applications.
\end{enumerate}
In addition 208 papers were presented
\begin{enumerate}
\item[a)] as communications in simultaneous subsections (112),
\item[b)] at the poster session (31),
\item[c)] in the form of enlarged abstracts (65).
\end{enumerate}

Besides the scientific program the participants could enjoy a
rich social program (e.g. Welcome Party at the Brno castle \v{S}pilberk,
Glass of wine and Concert, Audience with Mayor of Brno, Trips and
Farewell Party in wine cellar Queen Eli\v{s}ka).

This volume contains 12 survey papers mainly by the
plenary speakers.

Together  with  this  Proceedings  the following EQUADIFF 9 publications
have been prepared:
\begin{itemize}
\item[\textbullet]  EQUADIFF 9 issue of 
\href{http://www.emis.de/journals/AM/}{Archivum mathematicum} (Tomus 34, 1998, No.~1, 232~pp.) 
containing 20 papers by invited speakers (published in May 1998),
\item[\textbullet]  CD  ROM containing, in electronic form, an Equadiff 9 issue of Archivum
 mathematicum, the Proceedings  and 31 other papers submitted by the
 participants of the conference  as well as other conference  material
 (e.g.  Abstracts,  List  of participants, and Program).
\end{itemize}
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\noindent
Brno, May 1998\hfill                             Editors
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