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Extension of the existence theorems of Schmitt and Smith to perturbations of Fredholm operators with index zero. (Extension des théorèmes d’existence de Schmitt et Smith aux perturbations d’opérateurs de Fredholm d’indice zéro.) (French) Zbl 0772.47033
Dans leur article [Rocky Mt. J. Math. 12, 817-841 (1982; Zbl 0527.34017)], K. Schmitt et H. Smith ont formulé quelques résultats abstraits pour résoudre certains problèmes aux limites non linéaires pouvant se ramener au problème du point fixe. (P) x=f(x)f est telle que son image est contenue dans un ensemble qui possède certaines propriétés de compacité et d’homogénéité. Dans cet article, nous proposons d’étendre ces résultats de Schmitt-Smith en remplaçant dans (P) l’opérateur identité par un opérateur de Fredholm d’indice zéro. Notre approche se base essentiellement sur la théorie du degré de coïncidence.
MSC:
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47A53(Semi-)Fredholm operators; index theories
47H11Degree theory (nonlinear operators)