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title:  Continuous selections of solution sets to evolution equations 
authors:  Staicu, Vasile 
issue date:  1991 
publisher:  American Mathematical Society 
abstract:  We prove the existence of a continuous selection of the multivalued
map £ —»& ~(Ç), where ^"(i) is the set of all weak (resp. mild) solutions of
the Cauchy problem
x(t)€Ax(t) + F(t,x(t)), x(0)=i,
assuming that F is Lipschitzian with respect to x and A is a maximal
monotone map (resp. A is the infinitesimal generator of a C0semigroup). We
also establish an analog of Michael's theorem for the solution sets of the Cauchy
problem x(t) € F(t, x(t)), x(0) = £, . 
URI:  http://hdl.handle.net/10773/5105 
ISSN:  00029939 
publisher version/DOI:  http://www.ams.org/publications/journals/journalsframework/proc 
source:  Proceedings of the American Mathematical Society 
appears in collections  MAT  Artigos

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