Set differential equations in Frechet spaces

• Autorzy: Galanis G., N. , Bhaskar T., G. , Lakshmikantham V.
• 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 K_c(F) of all compact, convex subsets of a Frechet space, F, is realized as a projective limit of the semilinear metric spaces K_c(Eⁱ). Using the notion of Hukuhara derivative for maps with values in K_c(F), we prove the local and global existence theorems for an initial value problem associated with a set differential equation.

Słowa kluczowe

EN

set differential equations; Hukuhara derivative; projective limits; Frechet spaces

PL

granica projektywna; przestrzeń Frecheta

• Wydawca: De Gruyter
• 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,

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.