Contents

Introduction 1

Suggestions for th e reade r 5

Chapter I . Fredhol m mapping s of index zero and linear boundar y valu e problems 6

Chapter II . Degre e theory fo r som e classes of mappings 15

Chapter HI . Dualit y theorem s for severa l fixed point operator s associate d to periodi c

problems for ordinar y differentia l equation s 3

Chapter IV . Existenc e theorems for equation s in normed space s 4 2

Chapter V. Boundar y valu e problems fo r secon d orde r nonlinea r vecto r differentia l

equations 5

Chapter VI . Periodi c solutions o f ordinar y differentia l equation s with one-side d

growth restriction s 6 3

Chapter VII. Boun d set s for functiona l differentia l equation s 7 4

Chapter VIII. Th e index o f isolated zero s of som e mappings 8 3

Chapter IX . Bifurcatio n theor y 9

Chapter X . Periodi c solutions of autonomous ordinar y differentia l equation s aroun d

an equilibrium 9 9

References 109

v