Strong solutions of evolution equations governed by 𝑚-accretive operators and the Radon-Nikodým property

Deville, Robert

doi:10.1090/S0002-9939-1991-1045133-9

Strong solutions of evolution equations governed by $m$-accretive operators and the Radon-Nikodým property
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Proc. Amer. Math. Soc. 112 (1991), 1001-1008 Request permission

Abstract:

We construct, in every Banach space which fails the Radon-Nikodym property, a nonlinear operator $A$ which is $m$-accretive for some equivalent norm in $X$, such that the domain of $A$ is not a singleton and such that the only strong solutions of the equation $u’ + Au \backepsilon f$ are the constant ones.

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