Tytuł artykułu
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Abstrakty
We provide a generalization of a well known Krasnosel'skii theorem on continuity of the Nemytskii operator for functions taking values in separable Banach spaces. We follow the results obtained in [6] for the finite dimensional case.
Wydawca
Czasopismo
Rocznik
Tom
Strony
139--147
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
autor
- Faculty of Mathematics University of Łódź Banacha 22 90-238 Łódź
Bibliografia
- [1] Ambrosetti, A., Prodi, G., A Primer of Nonlinear Analysis, Cambridge Studies in Advanced Mathematics 34, Cambridge University Press, Cambridge, 1993.
- [2] Appell, J., Upper estimates for superposition operators and some applications, Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes 8(1) (1983), 149-159.
- [3] Barbu V., Precupanu, Th., Convexity and Optimization in Banach Spaces, Mathematics and its Applications 10, D. Reidel Publ. Comp., Dordrecht, 1986.
- [4] Brezis, H., Analyse fonctionelle: thiorie et applications, Masson, Paris, 1983.
- [5] Dinca, G., Pasca, D., Existence theorem of periodical solutions of Hamiltonian systems in infinite-dimensional Hilbert spaces, Differential Integral Equations 14(4) (2001), 405-426.
- [6] Evans, L. C., Partial Differential Equations, Graduate Studies in Mathematics 19, Amer. Math. Soc., Providence, RI, 1998.
- [7] Hille, E., Philips, R. S., Functional Analysis and Semi-groups, Amer. Math. Soc. Colloquium Publications 31, Providence, RI, 1957.
- [8] Idczak, D., Rogowski, A., On the Krasnosel’skii Theorem — a short proof and some generalization, J. Austral. Math. Soc. Ser. B, (to appear).
- [9] Krasnosel’skii, M. A., Topological Methods in the Theory of Nonlinear Integral Equa tions, A Pergamon Press Book The Macmillan Co., New York, 1964.
- [10] Lieb, E. H., Loss, M., Analysis, Graduate Studies in Mathematics 14, Amer. Math. Soc., Providence, RI, 1997.
- [11] Mawhin, J., Metody wariacyjne dla nieliniowych problemów Dirichleta (in Polish), WNT, Warszawa, 1994.
- [12] Mawhin, J., Willem, M., Critical Point Theory, Springer-Verlag, New York, 1989.
- [13] Nowakowski, A., Rogowski, A., On the new variational principles and duality for periodic solutions of Lagrange equations with superlinear nonlinearities, J. Math. Anal. Appl. 264 (2001), 168-181.
- [14] Yosida, K., Functional Analysis, Springer-Verlag, New York, 1974.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD6-0014-0024