- Tytuł:
- Knesers theorems for strong, weak and pseudo-solutions of ordinary differential equations in Banach spaces
- Autorzy:
-
Cichoń, Mieczysław
Kubiaczyk, Ireneusz - Powiązania:
- https://bibliotekanauki.pl/articles/1311465.pdf
- Data publikacji:
- 1995
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
set of solutions
pseudo-solutions
measures of weak noncompactness
Pettis integral - Opis:
- We investigate the structure of the set of solutions of the Cauchy problem x' = f(t,x), x(0) = x₀ in Banach spaces. If f satisfies a compactness condition expressed in terms of measures of weak noncompactness, and f is Pettis-integrable, then the set of pseudo-solutions of this problem is a continuum in $C_{w}(I,E)$, the space of all continuous functions from I to E endowed with the weak topology. Under some additional assumptions these solutions are, in fact, weak solutions or strong Carathéodory solutions, so we also obtain Kneser-type theorems for these classes of solutions.
- Źródło:
-
Annales Polonici Mathematici; 1995, 62, 1; 13-21
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Dostawca treści:
- Biblioteka Nauki
Artykuł