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Weak growth conditions for ODEs in pre-ordered Banach spaces

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Abstract.

Let E be a pre-ordered real Banach space and f:[0,T)×E→E a quasimontone increasing function. We prove one-sided estimates of the form ∂+q[y−x,f(t,y)−f(t,x)]≤α(t,q(y−x)) 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.

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  1. Mathematisches Institut I, Universität Karlsruhe, 76128, Karlsruhe, Germany

    Gerd Herzog & Roland Lemmert

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  1. Gerd Herzog
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  2. Roland Lemmert
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Correspondence to Gerd Herzog.

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Mathematics Subject Classification (2000): 34C11, 34C12, 34G20

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Herzog, G., Lemmert, R. Weak growth conditions for ODEs in pre-ordered Banach spaces. Math. Ann. 331, 75–86 (2005). https://doi.org/10.1007/s00208-004-0574-6

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  • DOI: https://doi.org/10.1007/s00208-004-0574-6

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