JournalszaaVol. 22 , No. 3DOI 10.4171/zaa/1166

About the Sign of Oriented Fredholm Operators between Banach Spaces

  • Pierluigi Benevieri

    Universita di Firenze, Italy
  • Massimo Furi

    Università di Firenze, Italy
  • Maria Patrizia Pera

    Universita di Firenze, Italy
  • Marco Spadini

    Universita di Firenze, Italy
About the Sign of Oriented Fredholm Operators between Banach Spaces cover

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 Crandall-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.