Preface

This monograph i s an expanded versio n of a CBM S series of lectures deliv-

ered in Miami in January, 1984. A s in the lectures » our goa l is to provide a n

introduction t o minimax methods in critical point theory and their applicatio n

to problems in differential equations . Th e presentation of the abstract minima x

theory i s essentially self-contained . Mos t o f the application s ar e to semilinea r

elliptic partial differential equation s and a basic knowledge of linear elliptic the-

ory is required for this material. A n overview is given of the subject matte r in

Chapter 1 and a detailed study is carried out in the chapters that follow .

Many friend s hav e contributed t o my study an d Organizatio n o f this mate-

rial. I thank in particular Antonio Ambrosetti, Abbas Bahri, Vieri Benci, Henri

Berestycki, Hai m Brezis , Michae l Crandall , Edwar d Fadell , Suffia n Husseini ,

Jürgen Moser , an d Loui s Nirenberg fo r thei r inspiration , encouragement , an d

advice. Th e CBMS Conference was hosted by the Mathematics Departmen t of

the University of Miami. Further thanks are due to the members of the depart-

ment, especially t o Shair Ahmad an d Alan Lazer for thei r efficient handlin g of

the meeting and their kind hospitality.

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