On the structure of the set of solutions of a Volterra integral equation in a Banach space
Annales Polonici Mathematici (1994)
- Volume: 59, Issue: 1, page 33-39
- ISSN: 0066-2216
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topKrzysztof Czarnowski. "On the structure of the set of solutions of a Volterra integral equation in a Banach space." Annales Polonici Mathematici 59.1 (1994): 33-39. <http://eudml.org/doc/262486>.
@article{KrzysztofCzarnowski1994,
abstract = {The set of solutions of a Volterra equation in a Banach space with a Carathéodory kernel is proved to be an $ℛ_δ$, in particular compact and connected. The kernel is not assumed to be uniformly continuous with respect to the unknown function and the characterization is given in terms of a B₀-space of continuous functions on a noncompact domain.},
author = {Krzysztof Czarnowski},
journal = {Annales Polonici Mathematici},
keywords = {Volterra integral equation in a Banach space; $ℛ_δ$-sets; solution set; nonlinear Volterra integral equation of the second kind; abstract Banach space; Carathéodory conditions},
language = {eng},
number = {1},
pages = {33-39},
title = {On the structure of the set of solutions of a Volterra integral equation in a Banach space},
url = {http://eudml.org/doc/262486},
volume = {59},
year = {1994},
}
TY - JOUR
AU - Krzysztof Czarnowski
TI - On the structure of the set of solutions of a Volterra integral equation in a Banach space
JO - Annales Polonici Mathematici
PY - 1994
VL - 59
IS - 1
SP - 33
EP - 39
AB - The set of solutions of a Volterra equation in a Banach space with a Carathéodory kernel is proved to be an $ℛ_δ$, in particular compact and connected. The kernel is not assumed to be uniformly continuous with respect to the unknown function and the characterization is given in terms of a B₀-space of continuous functions on a noncompact domain.
LA - eng
KW - Volterra integral equation in a Banach space; $ℛ_δ$-sets; solution set; nonlinear Volterra integral equation of the second kind; abstract Banach space; Carathéodory conditions
UR - http://eudml.org/doc/262486
ER -
References
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- [8] S. Szufla, On the structure of solution sets of differential and integral equations in Banach spaces, Ann. Polon. Math. 34 (1977), 165-177. Zbl0384.34038
- [9] G. Vidossich, On the structure of the set of solutions of nonlinear equations, J. Math. Anal. Appl. 34 (1971), 602-617.
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