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 1 5 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 1 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 1 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 1 Chapter X . Periodi c solutions of autonomous ordinar y differentia l equation s aroun d an equilibrium 9 9 References 10 9 v

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