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Title: Non-autonomous vector integral equations with discontinuous right-hand side (English)
Author: Cubiotti, Paolo
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 42
Issue: 2
Year: 2001
Pages: 319-329
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Category: math
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Summary: We deal with the integral equation $u(t)=f(t,\int_I g(t,z)u(z)\,dz)$, with $t\in I:=[0,1]$, $f:I\times \Bbb R^n \to \Bbb R^n$ and $g:I\times I\to[0,+\infty[$. We prove an existence theorem for solutions $u\in L^s(I,\Bbb R^n)$, $s\in \,]1,+\infty]$, where $f$ is not assumed to be continuous in the second variable. Our result extends a result recently obtained for the special case where $f$ does not depend explicitly on the first variable $t\in I$. (English)
Keyword: vector integral equations
Keyword: discontinuity
Keyword: multifunctions
Keyword: operator inclusions
MSC: 45G10
MSC: 45P05
MSC: 47H15
MSC: 47J05
MSC: 47N20
idZBL: Zbl 1055.45004
idMR: MR1832150
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Date available: 2009-01-08T19:10:15Z
Last updated: 2012-04-30
Stable URL: http://hdl.handle.net/10338.dmlcz/119246
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