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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-article-LOD6-0004-0009

Czasopismo

Journal of Applied Analysis

Tytuł artykułu

Set differential equations in Frechet spaces

Autorzy Galanis, G., N.  Bhaskar, T., G.  Lakshmikantham, V. 
Treść / Zawartość
Warianty tytułu
Języki publikacji EN
Abstrakty
EN It is known that a frachet space F can be realized as a projective limit of a sequence of Banach spaces Ei. The space Kc(F) of all compact, convex subsets of a Frechet space, F, is realized as a projective limit of the semilinear metric spaces Kc(Ei). Using the notion of Hukuhara derivative for maps with values in Kc(F), we prove the local and global existence theorems for an initial value problem associated with a set differential equation.
Słowa kluczowe
PL granica projektywna   przestrzeń Frecheta  
EN set differential equations   Hukuhara derivative   projective limits   Frechet spaces  
Wydawca Walter de Gruyter GmbH & Co. KG
Czasopismo Journal of Applied Analysis
Rocznik 2008
Tom Vol. 14, nr 1
Strony 103--113
Opis fizyczny Bibliogr. 7 poz.
Twórcy
autor Galanis, G., N.
autor Bhaskar, T., G.
autor Lakshmikantham, V.
  • Naval Academy of Greece. Section of Mathematics, Xatzikyriakion, Piraeus 185 39 Greece, ggalanis@snd.edu.gr
Bibliografia
[1] Galanis, G. N., On a type of linear differential equations in Frechet spaces, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 24(3) (1997), 501-510.
[2] Galanis, G. N., Bhaskar, T. Gnana, Lakshmikantham, V., Palamides, P. K., Set valued functions in Frechet spaces: continuity, Hukuhara differentiability and applications to set differential equations, Nonlinear Anal. 61(4) (2005), 559-575.
[3] Galanis, G. N., Palamides, P. K., Nonlinear differential equations in Frechet spaces and continuum cross-sections, An. Stiint. Univ. Al. I. Guza Iasi Mat. (N.S.) 51(1) (2005), 41-54.
[4] Hukuhara, M., Integration of measurable maps with compact, convex set values, Funk-cial. Ekvac. 10 (1967), 205-23.
[5] Lakshmikantham, V., Bhaskar, T. Gnana, Devi, J. Yasundhara, Theory of Set Differential Equations in a Metric Space, Cambridge Scientific Publ., Cambridge, 2006.
[6] Schaeffer, H. H., Topological Vector Spaces, Springer-Verlag, Berlin, 1980.
[7] Tolstonogov, A., Differential Inclusions in a Banach Space, Kluwer Acad. Publ., Dor-drecht, 2000.
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