Positivity of Maps and Applications

  • E. N. Dancer
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 15)


In this survey, we discuss some recent work on maps in cones on Banach spaces. We emphasize developments more recent than Amann’s survey article [2], and try to limit the intersection with Nussbaum’s survey [38]. We emphasize results which depend upon fixed point arguments. We also, at times, discuss applications to ordinary and partial differential equations. We do not discuss applications to delay equations. These are important but they tend to be outside the author’s expertise. We do, however, discuss applications to dynamical systems. We will use the fixed point index as a tool and we summarize its properties. A survey of the fixed point index for more general maps appears in Nussbaum [37].


Stationary Point Banach Lattice Continuous Case Point Index Order Interval 
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Copyright information

© Birkhäuser Boston 1995

Authors and Affiliations

  • E. N. Dancer
    • 1
  1. 1.Department of Mathematics, Statistics and Computing ScienceThe University of New EnglandArmidaleAustralia

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