Sous-Potentiels D’un Operateur Nonlineaire |
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Authors: | Louise Barthélemy Philippe Bénilan |
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Institution: | 1. Equipe de Mathématiques au Besan?on, CNRS, UA 741, Université de Franche-Compte, 25030, Besan?on Cedex, France
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Abstract: | LetA be a (nonlinear) operator in an ordered linear spaceX with resolvantJ
λ=(I+λA)-1 well-defined onX and non-decreasing for any smallλ>0, andν ∈X. We define sub-potential ofν with respect toA, as anyu ∈X satisfyingu≧J
λ(u+λv) for smallλ>0, and show that this coincides with the notion of sub-solution of the equationAu∋ν in some abstract cases where such notion is defined in a natural way. At last, we give some general properties of sub-potentials,
in particular an extension of the Kato inequality whenX is a lattice, and, for good set of constraintsU, existence of a largest solution for the control problem:u ∈U andu is a sub-potential ofν with respect toA.
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