We give conditions for an oriented family of bounded Fredholm operators of index zero between Banach spaces to have a sign jump. In particular, we discuss criteria for detecting the sign jump in some special situations. For instance, when a sort of C randall-Rabinowitz condition for bifurcation is assumed or in the case of a family of Leray-Schauder type. Finally, some examples of ordinary differential operators are presented to illustrate the meaning of the abstract results.
About the sign of oriented Fredholm operators between Banach spaces / P. Benevieri; M. Furi; M.P. Pera; M. Spadini. - In: ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN. - ISSN 0232-2064. - STAMPA. - 22:(2003), pp. 619-645. [10.4171/ZAA/1166]
About the sign of oriented Fredholm operators between Banach spaces
BENEVIERI, PIERLUIGI;FURI, MASSIMO;PERA, MARIA PATRIZIA;SPADINI, MARCO
2003
Abstract
We give conditions for an oriented family of bounded Fredholm operators of index zero between Banach spaces to have a sign jump. In particular, we discuss criteria for detecting the sign jump in some special situations. For instance, when a sort of C randall-Rabinowitz condition for bifurcation is assumed or in the case of a family of Leray-Schauder type. Finally, some examples of ordinary differential operators are presented to illustrate the meaning of the abstract results.
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