Geodesic
Non-autonomous implicit integral equations with discontinuous right-hand side
Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 3, pp. 417-429.

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We deal with the implicit integral equation $$ h(u(t))=f(\,t\,,\int_Ig(t,z)\,u(z)\,dz) \hbox{ for a.a. } t\in I, $$ where $I:=[0,1]$ and where $f:I\times [0,\lambda]\to{\Bbb R}$, $g:I\times I\to[0,+\infty[$ and $h:\,]\,0,+\infty\,[\,\to {\Bbb R}$. We prove an existence theorem for solutions $u\in L^s(I)$ where the contituity of $f$ with respect to the second variable is not assumed.
Classification : 45P05, 47G10, 47J05, 47N20
Keywords: implicit integral equations; discontinuity; lower semicontinuous multifunctions; operator inclusions; selections 
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     title = {Non-autonomous implicit integral equations with discontinuous right-hand side},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
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Anello, Giovanni; Cubiotti, Paolo. Non-autonomous implicit integral equations with discontinuous right-hand side. Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 3, pp. 417-429. http://geodesic.mathdoc.fr/item/CMUC_2004__45_3_a3/