The Henstock-Kurzweil-Pettis integrals and existence theorems for the Cauchy problem

Title:

The Henstock-Kurzweil-Pettis integrals and existence theorems for the Cauchy problem

Creator:

Cichoń, Mieczysław, Kubiaczyk, Ireneusz , and Sikorska-Nowak, Aneta

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:f28952ba-9b5c-402c-8cd7-f5fce6aeeb74
uuid:f28952ba-9b5c-402c-8cd7-f5fce6aeeb74

Subject:

pseudo-solution, Pettis integral, Henstock-Kurzweil integral, and Cauchy problem

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In this paper we prove an existence theorem for the Cauchy problem \[ x^{\prime }(t) = f(t, x(t)), \quad x(0) = x_0, \quad t \in I_{\alpha } = [0, \alpha ] \] using the Henstock-Kurzweil-Pettis integral and its properties. The requirements on the function $f$ are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose that the function $f$ satisfies some conditions expressed in terms of measures of weak noncompactness.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

279-289

Source:

Czechoslovak Mathematical Journal | 2004 Volume:54 | Number:2

Harvested from:

CDK

Metadata only:

false