Non-autonomous vector integral equations with discontinuous right-hand side

Cubiotti, Paolo. "Non-autonomous vector integral equations with discontinuous right-hand side." Commentationes Mathematicae Universitatis Carolinae 42.2 (2001): 319-329. <http://eudml.org/doc/248787>.

@article{Cubiotti2001,
abstract = {We deal with the integral equation $u(t)=f(t,\int _I g(t,z)u(z)\,dz)$, with $t\in I:=[0,1]$, $f:I\times \mathbb \{R\}^n \rightarrow \mathbb \{R\}^n$ and $g:I\times I\rightarrow [0,+\infty [$. We prove an existence theorem for solutions $u\in L^s(I,\mathbb \{R\}^n)$, $s\in \,]1,+\infty ]$, 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 $t\in I$.},
author = {Cubiotti, Paolo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {vector integral equations; discontinuity; multifunctions; operator inclusions; -solutions; nonlinearities; operator inclusion},
language = {eng},
number = {2},
pages = {319-329},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Non-autonomous vector integral equations with discontinuous right-hand side},
url = {http://eudml.org/doc/248787},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Cubiotti, Paolo
TI - Non-autonomous vector integral equations with discontinuous right-hand side
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 2
SP - 319
EP - 329
AB - We deal with the integral equation $u(t)=f(t,\int _I g(t,z)u(z)\,dz)$, with $t\in I:=[0,1]$, $f:I\times \mathbb {R}^n \rightarrow \mathbb {R}^n$ and $g:I\times I\rightarrow [0,+\infty [$. We prove an existence theorem for solutions $u\in L^s(I,\mathbb {R}^n)$, $s\in \,]1,+\infty ]$, 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 $t\in I$.
LA - eng
KW - vector integral equations; discontinuity; multifunctions; operator inclusions; -solutions; nonlinearities; operator inclusion
UR - http://eudml.org/doc/248787
ER -