Existence of global solutions to differential inclusions; a priori bounds

Ovidiu Cârjă; Alina Ilinca Lazu

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Displaying similar documents to “Existence of global solutions to differential inclusions; a priori bounds”

A generalization of the Schauder fixed point theorem via multivalued contractions

Paolo Cubiotti, Beatrice Di Bella (2001)

Commentationes Mathematicae Universitatis Carolinae

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We establish a fixed point theorem for a continuous function $f : X \to E$ , where $E$ is a Banach space and $X \subseteq E$ . Our result, which involves multivalued contractions, contains the classical Schauder fixed point theorem as a special case. An application is presented.

Implicit integral equations with discontinuous right-hand side

Filippo Cammaroto, Paolo Cubiotti (1997)

Commentationes Mathematicae Universitatis Carolinae

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We consider the integral equation $h (u (t)) = f (\int_{I} g (t, x) u (x) d x)$ , with $t \in [0, 1]$ , and prove an existence theorem for bounded solutions where $f$ is not assumed to be continuous.