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


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.


Banach Space Growth Condition Total Variation Function Space Real Banach Space 
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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Mathematisches Institut IUniversität KarlsruheKarlsruheGermany

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