# 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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- [3] K. Czarnowski and T. Pruszko, On the structure of fixed point sets of compact maps in B₀ spaces with applications to integral and differential equations in unbounded domain, J. Math. Anal. Appl. 154 (1991), 151-163. Zbl0729.47054
- [4] K. Deimling, Ordinary Differential Equations in Banach Spaces, Lecture Notes in Math. 596, Springer, Berlin, 1977.
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- [6] H. P. Heinz, On the behaviour of measures of noncompactness with respect to differentiation and integration of vector-valued functions, Nonlinear Anal. 7 (1983), 1351-1371. Zbl0528.47046
- [7] J. M. Lasry et R. Robert, Analyse non linéaire multivoque, Centre de Recherche de Math. de la Décision, No. 7611, Université de Paris-Dauphine.
- [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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