A nonlinear version of the Kantorovich-Rubinstein maximum principle

  • Authors:

  • Henryk Gacki;Andrzej Lasota

  • Affiliations:

  • Institute of Mathematics, Silesian University Bankowa 14, 40-007 Katowice, Poland;Institute of Mathematics, Silesian University Bankowa 14, 40-007 Katowice, Poland

  • Venue:
  • Nonlinear Analysis: Theory, Methods & Applications - Theory and methods
  • Year:
  • 2003

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Abstract

The classical Kantorovich-Rubinstein theory gives necessary conditions for maxima of linear functionals acting on the space of Lipsehitzian functions. We show analogous results for some nonlinear functionals of Hammerstein type. Our proofs are based on theorems concerning local changes of Lipschitzian functions similar to the McShane extension theorem.