Abstract: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 $n=1$.
Keywords: vector integral equations, bounded solutions, discontinuity
AMS Subject Classification: 47H15