Kneser's theorems for strong, weak and pseudo-solutions of ordinary differential equations in Banach spaces

• Autorzy: Mieczysław Cichoń , Ireneusz Kubiaczyk
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

set of solutions; pseudo-solutions; measures of weak noncompactness; Pettis integral

Kategorie tematyczne

• 47H09: Contraction-type mappings, nonexpansive mappings, A -proper mappings, etc.
• 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1995
• Tom: 62
• Numer: 1
• Strony: 13-21

Daty

wydano

1995

otrzymano

1993-06-20

Twórcy

autor

Mieczysław Cichoń

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland

autor

Ireneusz Kubiaczyk

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland

Bibliografia

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