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In the present paper initial value problems x = f (t, x), t ϵ I = [0, 1], x (0) = xo in Banach lattices will be investigated with respect to order and topological properties of their solution sets S (f) C ⊆ (I, X).
Słowa kluczowe
Wydawca
Rocznik
Tom
Strony
113--124
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
autor
- Fakultät für Mathematik, Universität Karlsruhe, D-76128 Karlsruhe, Germany, herbert.weigel@math.uni-karlsruhe.de
Bibliografia
- [1] N. Aronszajn, Le correspondant topologique de l’unicité, Ann. Math. 43 (1942), 730-738.
- [2] E. Bohl, Monotonie: Lösbarkeit und Numerik bei Operatorgleichungen, Springer-Verlag, 1974.
- [3] A. Chaljub-Simon and P. Volkmann, Ordinary differential equations in Banach spaces with variable order cones, WSSIAA 1 (1992), 63-70.
- [4] K. Deimling, Ordinary Differential Equations in Banach Spaces, Lect. Notes Math. 596, Springer-Verlag, 1977.
- [5] G. Herzog, A funnel section property for systems with quasimonotone increasing right hand side, Glasgow Math. J. 42 (2000), 239-242.
- [6] G. Herzog and R. Lemmert, On the structure of the solution set of u" = f (t, u), u (0) = u (l) = 0, Math. Nachr. 215 (2000), 103-105.
- [7] G. Herzog and R. Lemmert, On maximal and minimal solutions for x' (t) = F (t, x(t), x(h(t))), x (0) = x0, Comment. Math. Prace Matem. 40 (2000), 93-102.
- [8] M. Hukuhara, Sur les systèmes des équations différentielles ordinaires, Proc. Imp. Acad. Japan 4 (1928), 448-449.
- [9] C. C. Pugh, Funnel sections, J. Differ. Equations 19 (1975), 270-295.
- [10] H. H. Schaefer, Topological Vector Spaces, Macmillan, New York, 1980.
- [11] P. Volkmann, Gewöhnliche Differentialungleichungen mit quasimonoton wachsenden Funktionen in topologischen Vektorräumen, Math. Z. 127 (1972), 157-164.
- [12] W. Walter, Ordinary Differential Equations, Graduate Texts in Mathematics 182, Springer-Verlag, New York, 1998.
- [13] H. Weigel, A topological property of the solution funnel of x' = ƒ(t, x), x(0) = x0, Nonlinear Analysis 49 (2002), 1105-1109.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-BUS2-0002-0051