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Multi-valued perturbation to evolution problems involving time dependent maximal monotone operators

  • * Corresponding author: Dalila Azzam-Laouir

    * Corresponding author: Dalila Azzam-Laouir 
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  • In this paper, we study the existence of solutions for evolution problems of the form $ -\frac{du}{dr}(t) \in A(t)u(t) + F(t, u(t))+f(t, u(t)) $, where, for each $ t $, $ A(t) : D(A(t)) \to 2 ^H $ is a maximal monotone operator in a Hilbert space $ H $ with continuous, Lipschitz or absolutely continuous variation in time. The perturbation $ f $ is separately integrable on $ [0, T] $ and separately Lipschitz on $ H $, while $ F $ is scalarly measurable and separately scalarly upper semicontinuous on $ H $, with convex and weakly compact values. Several new applications are provided.

    Mathematics Subject Classification: Primary: 34A60, 28C20; Secondary: 28A25.


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