Giovanni Anello, Paolo Cubiotti
Non-autonomous implicit integral equations with discontinuous right-hand side

Comment.Math.Univ.Carolinae 45,3 (2004) 417-429.

Abstract: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.

Keywords: implicit integral equations, discontinuity, lower semicontinuous multifunctions, operator inclusions, selections
AMS Subject Classification: 45P05, 47G10