A note on a non-linear Krein–Rutman theorem

  title={A note on a non-linear Krein–Rutman theorem},
  author={Rajesh Mahadevan},
  journal={Nonlinear Analysis-theory Methods \& Applications},
  • R. Mahadevan
  • Published 2006
  • Mathematics
  • Nonlinear Analysis-theory Methods & Applications
Abstract In this note we will present an extension of the Krein–Rutman theorem [M.G. Kreĭn, M.A. Rutman, Linear operators leaving invariant a cone in a Banach space, Amer. Math. Soc. Transl. (26) (1950). [9] ] for an abstract non-linear, compact, positively 1-homogeneous operator on a Banach space having the properties of being increasing with respect to a convex cone K and such that there is a non-zero u ∈ K for which M T u ≽ u for some positive constant M . This will provide a uniform… Expand
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