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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

Similarity:

We consider a multifunction F : T × X 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

Similarity:

Let D T × 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

Similarity:

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