Implicit integral equations with discontinuous right-hand side

Filippo Cammaroto; Paolo Cubiotti

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 2, page 241-246
  • ISSN: 0010-2628

Abstract

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We consider the integral equation h ( u ( t ) ) = f ( ∫ I g ( t , x ) u ( x ) d x ) , with t ∈ [ 0 , 1 ] , and prove an existence theorem for bounded solutions where f is not assumed to be continuous.

How to cite

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Cammaroto, Filippo, and Cubiotti, Paolo. "Implicit integral equations with discontinuous right-hand side." Commentationes Mathematicae Universitatis Carolinae 38.2 (1997): 241-246. <http://eudml.org/doc/248053>.

@article{Cammaroto1997,
abstract = {We consider the integral equation $h(u(t))=f\big (\int _I g(t,x)\,u(x)\,dx\big )$, with $t\in [0,1]$, and prove an existence theorem for bounded solutions where $f$ is not assumed to be continuous.},
author = {Cammaroto, Filippo, Cubiotti, Paolo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {integral equations; discontinuity; bounded solutions; bounded solutions; integral equations; discontinuous right-hand side},
language = {eng},
number = {2},
pages = {241-246},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Implicit integral equations with discontinuous right-hand side},
url = {http://eudml.org/doc/248053},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Cammaroto, Filippo
AU - Cubiotti, Paolo
TI - Implicit integral equations with discontinuous right-hand side
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 2
SP - 241
EP - 246
AB - We consider the integral equation $h(u(t))=f\big (\int _I g(t,x)\,u(x)\,dx\big )$, with $t\in [0,1]$, and prove an existence theorem for bounded solutions where $f$ is not assumed to be continuous.
LA - eng
KW - integral equations; discontinuity; bounded solutions; bounded solutions; integral equations; discontinuous right-hand side
UR - http://eudml.org/doc/248053
ER -

References

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  13. Saint Raymond J., Riemann-measurable selections, Set-Valued Anal. 2 (1994), 481-485. (1994) Zbl0851.54021MR1304050
  14. Villani A., On Lusin's condition for the inverse function, Rend. Circ. Mat. Palermo 33 (1984), 331-335. (1984) Zbl0562.26002MR0779937

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