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Mathematische Annalen

, Volume 331, Issue 1, pp 75–86 | Cite as

Weak growth conditions for ODEs in pre-ordered Banach spaces

  • Gerd HerzogEmail author
  • Roland Lemmert
Article

Abstract.

Let E be a pre-ordered real Banach space and f:[0,TEE a quasimontone increasing function. We prove one-sided estimates of the form ∂+q[yx,f(t,y)−f(t,x)]≤α(t,q(yx)) with respect to seminorms q generated by a single positive linear functional. Such estimates lead to growth conditions, for example for the total variation of the solution of u′=f(t,u) in function spaces.

Keywords

Banach Space Growth Condition Total Variation Function Space Real Banach Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Mathematisches Institut IUniversität KarlsruheKarlsruheGermany

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