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596 Klaus Deimling

Ordinary Differential Equations in Banach Spaces

Springer-Verlag Berlin. Heidelberg New York 1977

Author Klaus Deimling Fachbereich 17 der G e s a m t h o c h s c h u l e Warburger Stra6e 100 D - 4 7 9 0 Paderborn

Library of Congress Cataloging in Publication Data

Deimling, K l a u s , 1953Ordina¢7 differential equations in Banaeh s p a c e s . (~ecture notes in mathematics ; 596) Bibliography: p. Includes index. i. Differential equations. 2. Nanach spaces. I. Title. II. Series: Lecture notes in mathematics

( ~ r ~ i n ) ; 5%.

q,&3.I28 no. 5£6 [~&372] 510'.8s [53-5'352] 77-22408

AMS Subject Classifications (1970): 34 G 05, 34 F 05, 47 H 10, 47 H 15, 60J80, 65J05 ISBN 3-540-08260-3 Springer-Verlag Berlin - Heidelberg • New York ISBN 0-387-08260-3 Springer-Verlag New York • Heidelberg • Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Vertag Berlin • Heidelberg 197? Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210

Preface

These

notes

represent

one-semester

at the U n i v e r s i t y less

recent

analysis

an e x p a n d e d

graduate

level

of K i e l

connections

without

and w i t h m a i n

emphasis

in 1975

between

assuming

version

course

of m a t e r i a l

on d i f f e r e r e n t i a l . The

aim has

differential

too many

been

systems

for a held

to s h o w m o r e

equations

prerequisites

on c o u n t a b l e

prepared equations

from

or

and f u n c t i o n a l both

of o r d i n a r y

fields

,

differential

equations. In the m a i n tions least

reference

not

troversy do we

in the

§ 4

The

further Having

informed and

finished

(UCLA)

Martin

has

that been

by Frof.

M.

§ 6 - ~ 7 overlap

Finally,

I want

eliminated in the

and

Prof.

A.

[113]

to send me

Kwapisz

(Gdansk)

on c o u n t a b l e

in s e v e r a l Jan

mistakes, Dold

Notes

book

for

Pr~

that with

was

the

with

who read

the p o s s i b i l i t y

existence Naturally,

the

Brigitte

by Prof.

Hereafter,

[113]

and

entire for

and

Klaus

, resand

the m a n u s -

the m a n u s c r i p t

Deimlin@ April

book

§ 2 - § 5

manuscript

to p u b l i s h

R.

Prof.

of the

[199]

typinz

to

we w e r e

series.

Paderborn,

A (i)

as a g u i d e

in the b e i n ~

systems.

con-

result.

in R e m a r k

informed

a copy.

or at

no r e f e r e n c e

of a c e r t a i n

been

Results

or n e w

to p r e v e n t

is m e n t i o n e d

about

topics

my wife

chapter,

a l s o be u n d e r s t o o d

§ 1 - ~ 7 we h a v e

GeneraliZa-

trivial

In o r d e r

place

uncertainty

§ 8 sho