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Existence theory for semilinear evolution inclusions involving measures
Author(s) -
Cichoń Mieczysław,
Satco Bianca
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600162
Subject(s) - mathematics , banach space , compact space , separable space , pure mathematics , infinitesimal , generator (circuit theory) , differential inclusion , fixed point theorem , semigroup , fixed point , space (punctuation) , mathematical analysis , power (physics) , linguistics , physics , philosophy , quantum mechanics
We provide existence results for semilinear differential inclusions involving measures: 0.1d u ∈ A ud t + F ( t , u ) d g , t ∈ [ 0 , 1 ] ,u ( 0 ) = u 0 ,where A is the infinitesimal generator of a C 0 ‐semigroup { T ( t ) , t ≥ 0 } of contractions on a separable Banach space X and g : [ 0 , 1 ] → R is a right‐continuous non‐decreasing function. The existence of mild solutions, as well as the compactness of the solution set are obtained via Kakutani–Ky Fan's fixed point theorem in the space of regulated functions endowed with weak, respectively strong topologies. Some examples of special cases covered by our existence results have been included.