Archiv der Mathematik

, Volume 70, Issue 2, pp 142–146 | Cite as

On ordinary differential equations with quasimonotone increasing right-hand side

  • Gerd Herzog


We prove that the initial value problem x ' (t) = f (t,x (t)), \( t \in [0,T] \), x (0) = x 0, is uniquely solvable in certain ordered Banach spaces if, f is quasimonotone increasing with respect to x, and if f is satisfying a one-sided Lipschitz condition with respect to the order-inducing cone.


Differential Equation Banach Space Ordinary Differential Equation Lipschitz Condition Order Banach Space 
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Copyright information

© Birkhäuser Verlag, Basel 1998

Authors and Affiliations

  • Gerd Herzog
    • 1
  1. 1.Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, GermanyDE

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