Existence of global solutions to differential inclusions; a priori bounds

Ovidiu Cârjă; Alina Ilinca Lazu

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.

Asymptotic behavior of positive solutions of a Dirichlet problem involving supercritical nonlinearities

Giovanni Anello, Giuseppe Rao (2013)

Commentationes Mathematicae Universitatis Carolinae

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Let $p > 1$ , $q > p$ , $λ > 0$ and $s \in] 1, p [$ . We study, for $s \to p^{-}$ , the behavior of positive solutions of the problem $- Δ_{p} u = λ u^{s - 1} + u^{q - 1}$ in $Ω$ , $u_{∣ \partial Ω} = 0$ . In particular, we give a positive answer to an open question formulated in a recent paper of the first author.

A note on splittable spaces

Vladimir Vladimirovich Tkachuk (1992)

Commentationes Mathematicae Universitatis Carolinae

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A space $X$ is splittable over a space $Y$ (or splits over $Y$ ) if for every $A \subset X$ there exists a continuous map $f : X \to Y$ with $f^{- 1} f A = A$ . We prove that any $n$ -dimensional polyhedron splits over $𝐑^{2 n}$ but not necessarily over $𝐑^{2 n - 2}$ . It is established that if a metrizable compact $X$ splits over $𝐑^{n}$ , then $dim X \leq n$ . An example of $n$ -dimensional compact space which does not split over $𝐑^{2 n}$ is given.