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

Giovanni Anello; Paolo Cubiotti

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 3, page 417-429
  • ISSN: 0010-2628

Abstract

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We deal with the implicit integral equation h ( u ( t ) ) = f ( t , ∫ I g ( t , z ) u ( z ) d z ) for a.a. t ∈ I , where I : = [ 0 , 1 ] and where f : I × [ 0 , λ ] → ℝ , g : I × I → [ 0 , + ∞ [ and h : ] 0 , + ∞ [ → ℝ . We prove an existence theorem for solutions u ∈ L s ( I ) where the contituity of f with respect to the second variable is not assumed.

How to cite

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Anello, Giovanni, and Cubiotti, Paolo. "Non-autonomous implicit integral equations with discontinuous right-hand side." Commentationes Mathematicae Universitatis Carolinae 45.3 (2004): 417-429. <http://eudml.org/doc/249338>.

@article{Anello2004,
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 $f:I\times [0,\lambda ]\rightarrow \{\mathbb \{R\}\}$, $g:I\times I\rightarrow [0,+\infty [$ and $h:\,]\,0,+\infty \,[\,\rightarrow \{\mathbb \{R\}\}$. 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.},
author = {Anello, Giovanni, Cubiotti, Paolo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {implicit integral equations; discontinuity; lower semicontinuous multifunctions; operator inclusions; selections; implicit integral equations; discontinuity; lower semicontinuous multifunction; operator inclusion; selection; existence},
language = {eng},
number = {3},
pages = {417-429},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Non-autonomous implicit integral equations with discontinuous right-hand side},
url = {http://eudml.org/doc/249338},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Anello, Giovanni
AU - Cubiotti, Paolo
TI - Non-autonomous implicit integral equations with discontinuous right-hand side
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 3
SP - 417
EP - 429
AB - 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 $f:I\times [0,\lambda ]\rightarrow {\mathbb {R}}$, $g:I\times I\rightarrow [0,+\infty [$ and $h:\,]\,0,+\infty \,[\,\rightarrow {\mathbb {R}}$. 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.
LA - eng
KW - implicit integral equations; discontinuity; lower semicontinuous multifunctions; operator inclusions; selections; implicit integral equations; discontinuity; lower semicontinuous multifunction; operator inclusion; selection; existence
UR - http://eudml.org/doc/249338
ER -

References

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