Weak solutions of differential equations in Banach spaces

• Autorzy: Mieczysław Cichoń
• Języki publikacji: EN

Abstrakty

EN

In this paper we prove a theorem for the existence of pseudo-solutions to the Cauchy problem, x' = f(t,x), x(0) = x₀ in Banach spaces. The function f will be assumed Pettis-integrable, but this assumption is not sufficient for the existence of solutions. We impose a weak compactness type condition expressed in terms of measures of weak noncompactness. We show that under some additionally assumptions our solutions are, in fact, weak solutions or even strong solutions. Thus, our theorem is an essential generalization of previous results.

Słowa kluczowe

EN

pseudo-solutions; Cauchy problem; measures of noncompactness

Kategorie tematyczne

• 47G10: Integral operators
• 28B05: Vector-valued set functions, measures and integrals
• 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 1995
• Tom: 15
• Numer: 1
• Strony: 5-14

Daty

wydano

1995

Twórcy

autor

Mieczysław Cichoń

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

Bibliografia

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