Vector integral equations with discontinuous right-hand side

Filippo Cammaroto; Paolo Cubiotti

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 3, page 483-490
  • ISSN: 0010-2628

Abstract

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We deal with the integral equation u ( t ) = f ( ∫ I g ( t , z ) u ( z ) d z ) , with t ∈ I = [ 0 , 1 ] , f : 𝐑 n → 𝐑 n and g : I × I → [ 0 , + ∞ [ . We prove an existence theorem for solutions u ∈ L ∞ ( I , 𝐑 n ) where the function f is not assumed to be continuous, extending a result previously obtained for the case n = 1 .

How to cite

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Cammaroto, Filippo, and Cubiotti, Paolo. "Vector integral equations with discontinuous right-hand side." Commentationes Mathematicae Universitatis Carolinae 40.3 (1999): 483-490. <http://eudml.org/doc/248419>.

@article{Cammaroto1999,
abstract = {We deal with the integral equation $u(t)=f(\int _Ig(t,z)\,u(z)\,dz)$, with $t\in I=[0,1]$, $f:\mathbf \{R\}^n\rightarrow \mathbf \{R\}^n$ and $g:I\times I\rightarrow [0,+\infty [$. We prove an existence theorem for solutions $u\in L^\infty (I,\mathbf \{R\}^n)$ where the function $f$ is not assumed to be continuous, extending a result previously obtained for the case $n=1$.},
author = {Cammaroto, Filippo, Cubiotti, Paolo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {vector integral equations; bounded solutions; discontinuity; vector integral equations; bounded solutions; discontinuity; multifunction},
language = {eng},
number = {3},
pages = {483-490},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Vector integral equations with discontinuous right-hand side},
url = {http://eudml.org/doc/248419},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Cammaroto, Filippo
AU - Cubiotti, Paolo
TI - Vector integral equations with discontinuous right-hand side
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 3
SP - 483
EP - 490
AB - We deal with the integral equation $u(t)=f(\int _Ig(t,z)\,u(z)\,dz)$, with $t\in I=[0,1]$, $f:\mathbf {R}^n\rightarrow \mathbf {R}^n$ and $g:I\times I\rightarrow [0,+\infty [$. We prove an existence theorem for solutions $u\in L^\infty (I,\mathbf {R}^n)$ where the function $f$ is not assumed to be continuous, extending a result previously obtained for the case $n=1$.
LA - eng
KW - vector integral equations; bounded solutions; discontinuity; vector integral equations; bounded solutions; discontinuity; multifunction
UR - http://eudml.org/doc/248419
ER -

References

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