Displaying similar documents to “An existence theorem for Hammerstein integral equations.”

Kneser-type theorem for the Darboux problem in Banach spaces

Mieczysław Cichoń, Ireneusz Kubiaczyk (2001)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we study the Darboux problem in some class of Banach spaces. The right-hand side of this problem is a Pettis-integrable function satisfying some conditions expressed in terms of measures of weak noncompactness. We prove that the set of all local pseudo-solutions of our problem is nonempty, compact and connected in the space of continuous functions equipped with the weak topology.

Integrable solutions of a functional-integral equation.

Józef Banas, Zygmunt Knap (1989)

Revista Matemática de la Universidad Complutense de Madrid

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This paper contains a theorem on the existence of monotonic and integrable solutions of a functional-integral equation. The proof of that theorem is based on the technique associated with the notion of a measure of weak noncompactness.