Sous-potentiels d'un opérateur nonlinéaire. (Subpotentials of a nonlinear operator)
Let X be an ordered linear space and A be a nonlinear operator in X such that \((I+\lambda A)^{-1}\) is defined and non-decreasing for small \(\lambda >0\). Given \(v\in X\), any element \(u\in X\) satisfying \(u\leq (I+\lambda A)^{-1}(u+\lambda v)\) is called sub-potential of v. The authors study some properties of sub-potentials, as well as relations with subsolutions of the problem Au\(\ni v\). Moreover, they obtain a ``nonlinear analogue of the Kato inequality [see e.g. \textit{W. Arendt}, ``One-parameter semigroups of positive operators'', Lect. Notes Math. 1184 (1986; Zbl 0585.47030)].
nonlinear analogue of the Kato inequality
scientific article; zbMATH DE number 4042644
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