Non-autonomous implicit integral equations with discontinuous right-hand side

Giovanni Anello; Paolo Cubiotti

Displaying similar documents to “Non-autonomous implicit integral equations with discontinuous right-hand side”

Parametrization of Riemann-measurable selections for multifunctions of two variables with application to differential inclusions

Giovanni Anello, Paolo Cubiotti (2004)

Annales Polonici Mathematici

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We consider a multifunction $F : T \times X \to 2^{E}$ , where T, X and E are separable metric spaces, with E complete. Assuming that F is jointly measurable in the product and a.e. lower semicontinuous in the second variable, we establish the existence of a selection for F which is measurable with respect to the first variable and a.e. continuous with respect to the second one. Our result is in the spirit of [11], where multifunctions of only one variable are considered.

Normal integrands and related classes of functions

Anna Kucia, Andrzej Nowak (1995)

Commentationes Mathematicae Universitatis Carolinae

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Let $D \subset T \times X$ , where $T$ is a measurable space, and $X$ a topological space. We study inclusions between three classes of extended real-valued functions on $D$ which are upper semicontinuous in $x$ and satisfy some measurability conditions.

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.

Semicontinuous integrands as jointly measurable maps

Oriol Carbonell-Nicolau (2014)

Commentationes Mathematicae Universitatis Carolinae

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Suppose that $(X, 𝒜)$ is a measurable space and $Y$ is a metrizable, Souslin space. Let $𝒜^{u}$ denote the universal completion of $𝒜$ . For $x \in X$ , let $\underset{̲}{f} (x, \cdot)$ be the lower semicontinuous hull of $f (x, \cdot)$ . If $f : X \times Y \to \bar{ℝ}$ is $(𝒜^{u} \otimes ℬ (Y), ℬ (\bar{ℝ}))$ -measurable, then $\underset{̲}{f}$ is $(𝒜^{u} \otimes ℬ (Y), ℬ (\bar{ℝ}))$ -measurable.

An existence theorem for an implicit integral equation with discontinuous right-hand side.

Anello, Giovanni (2006)

Journal of Inequalities and Applications [electronic only]

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