Suggestions for the reader This monograph i s planned t o b e read withou t a preliminary knowledg e o f degre e theory, although in severa l places lengthy technica l development s o r proof s o f difficul t re - sults have been omitted . Thes e gaps can be filled by consultin g the quote d literature . More - over, the require d basi c facts abou t ordinar y an d functiona l differentia l equation s ar e re- called, and som e familiarit y wit h thi s domai n o f analysi s is of cours e helpful . Chapter I and § § 1 and 2 of Chapte r I I should b e read regardles s of the reader' s in- terest i n the remaining chapters , and we shall call it th e basi c background. Th e reader in- terested i n dualit y theorem s for periodi c problems will complet e thi s basic background b y the readin g of § §4 an d 5 of Chapte r I I and o f Chapte r III . Fo r th e stud y o f existenc e theorems in differentia l equations , the reade r wil l add to th e basi c background th e stud y o f §3 o f Chapter II , and that o f Chapter s I V to VII , Chapters V, VI and VI I being, moreover, essentially independen t o f eac h other. A reader mainl y intereste d i n bifurcatio n theor y an d its applications will add to th e basic background th e readin g of Chapter s VIII to X. Each chapter i s followed b y historical an d bibliographica l note s with reference s t o th e bibliography give n at th e en d o f th e volume. Beside s quoting th e book s and papers directl y related t o the conten t o f thi s monograph, the lis t o f reference s give n here intend s to com - plete (an d no t t o reproduce ) th e on e given in the recen t boo k [84 ] o f Gaine s and th e author, where th e intereste d reade r ca n moreover find man y othe r application s treate d i n the spiri t o f thi s monograph .
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