| Title:
|
On the connectedness of the set of fixed points of a compact operator in the Fréchet space $C^m(\langle b,\infty),\bold R^n)$ (English) |
| Author:
|
Šeda, Valter |
| Author:
|
Kubáček, Zbyněk |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
42 |
| Issue:
|
4 |
| Year:
|
1992 |
| Pages:
|
577-588 |
| . |
| Category:
|
math |
| . |
| MSC:
|
34K05 |
| MSC:
|
46A04 |
| MSC:
|
47H10 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 0793.47055 |
| idMR:
|
MR1182189 |
| DOI:
|
10.21136/CMJ.1992.128365 |
| . |
| Date available:
|
2009-09-24T09:24:18Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128365 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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[3] Belohorec, Š.: Generalization of a certain theorem of N. Aroszajn and its application in the theory of functional differential equations.Manuscript. (Slovak) |
| Reference:
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[4] Browder, F. E., and Gupta, G. P.: Topological degree and non-linear mappings of analytic type in Banach spaces.Math. Anal. Appl. 26 (1969), 390–402. MR 0257826, 10.1016/0022-247X(69)90162-0 |
| Reference:
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[5] Czarnowski, K., and Pruszko, T.: On the structure of fixed point sets of compact maps in $B_0$ spaces with applications to integral and differential equations in unbounded domain.J. Math. Anal. Appl. 54 (1991), 151–163. MR 1087965, 10.1016/0022-247X(91)90077-D |
| Reference:
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[6] Deimling, K.: Nichtlineare Gleichungen und Abbildungsgrade.Springer–Verlag, Berlin Heidelberg New York, 1974. Zbl 0281.47033, MR 0500322 |
| Reference:
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[7] Hukuhara, M.: Sur une généralization d’un thèoreme de Kneser.Proc. Japan Acad. 29 (154–155). MR 0060084 |
| Reference:
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[8] Krasnoselski, M. A., Perov, A. I.: O sushchestvovanii resheni u nekotorykh nelinenykh operatornykh uravneni.Doklady AN SSSR 126 (1959), 15–18. MR 0106421 |
| Reference:
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[9] Krasnoselski, M. A., Zabreko, P. P.: Geometricheskie metody nelinenogo analiza.Nauka, Moskva, 1975. MR 0500310 |
| Reference:
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[10] Kubáček, Z.: A generalization of N. Aronszajn’s theorem on connectedness of the fixed point set of a compact mapping.Czechoslovak Math. J. 37 (112) (1987), 415–423. MR 0904769 |
| Reference:
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[11] Kuratowski, C.: Topologie, Volume II.Pol. Tow. Mat., Warszawa, 1952. |
| Reference:
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[12] Morales, P.: Topological properties of the set of global solutions for a class of semilinear evolution equations in a Banach space. Atti del Convegno celebrativo del $1^0$ centenario del Circolo Matematico di Palermo.Suppl. di Rendiconti del Circolo Matematico di Palermo, Serio II 8 (1985), 379–397. MR 0881416 |
| Reference:
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[13] Sadovski, V. N.: Predelno kompaktnye i uplotnyayushchie operatory.Uspekhi mat. nauk 27:1 (1972), 81–146. |
| Reference:
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[14] Stampacchia, G.: Le transformazioni che presentano il fenomeno di Peano.Rend. Accad. Naz Lincei 7 (1949), 80–84. MR 0033448 |
| Reference:
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[15] Szufla, S.: On the structure of solution sets of differential and integral equations in Banach spaces.Ann. Polon. Math XXXIV (1977), 165–177. MR 0463608, 10.4064/ap-34-2-165-177 |
| Reference:
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[16] Szufla, S.: On Volterra integral equations in Banach spaces.Funkcialaj Ekvacioj 20 (1977), 247–258. Zbl 0379.45025, MR 0511230 |
| Reference:
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[17] Szufla, S.: Sets of fixed points of nonlinear mappings in function spaces.Funkcialaj Ekvacioj 22 (1979), 121–126. Zbl 0419.47025, MR 0551256 |
| Reference:
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[18] Szufla, S.: On the existence of $L^p$-solutions of Volterra integral equations in Banach spaces.Funkcialaj Ekvacioj 27 (1984), 157–172. MR 0775204 |
| Reference:
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[19] Vidossich, G.: On the structure of the set of solutions of nonlinear equations.J. Math. Anal. Appl. 34 (1971), 602–617. MR 0283645, 10.1016/0022-247X(71)90100-4 |
| Reference:
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[20] Zeidler, E.: Vorlesungen über nichtlineare Funktionalanalysis I — Fixpunktsätze.Teubner Verlagsgesellschaft, Leipzig, 1976. Zbl 0326.47053, MR 0473927 |
| . |
