Geodesic
Vector integral equations with discontinuous right-hand side
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 3, pp. 483-490 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We deal with the integral equation $u(t)=f(\int_Ig(t,z)\,u(z)\,dz)$, with $t\in I=[0,1]$, $f:\bold R^n\to\bold R^n$ and $g:I\times I\to[0,+\infty[$. We prove an existence theorem for solutions $u\in L^\infty(I,\bold R^n)$ where the function $f$ is not assumed to be continuous, extending a result previously obtained for the case $n=1$.
We deal with the integral equation $u(t)=f(\int_Ig(t,z)\,u(z)\,dz)$, with $t\in I=[0,1]$, $f:\bold R^n\to\bold R^n$ and $g:I\times I\to[0,+\infty[$. We prove an existence theorem for solutions $u\in L^\infty(I,\bold R^n)$ where the function $f$ is not assumed to be continuous, extending a result previously obtained for the case $n=1$.
Classification : 45G10, 47H04, 47H15, 47J05, 47N20
Keywords: vector integral equations; bounded solutions; discontinuity 
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     author = {Cammaroto, Filippo and Cubiotti, Paolo},
     title = {Vector integral equations with discontinuous right-hand side},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {483--490},
     year = {1999},
     volume = {40},
     number = {3},
     mrnumber = {1732487},
     zbl = {1065.47505},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1999_40_3_a7/}
}
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Cammaroto, Filippo; Cubiotti, Paolo. Vector integral equations with discontinuous right-hand side. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 3, pp. 483-490. http://geodesic.mathdoc.fr/item/CMUC_1999_40_3_a7/