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

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

Czechoslovak Mathematical Journal (2004)

  • Volume: 54, Issue: 2, page 279-289
  • ISSN: 0011-4642

Abstract

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In this paper we prove an existence theorem for the Cauchy problem x ' ( t ) = f ( t , x ( t ) ) , x ( 0 ) = x 0 , t ∈ I α = [ 0 , α ] 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.

How to cite

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Cichoń, Mieczysław, Kubiaczyk, Ireneusz, and Sikorska-Nowak, Aneta, Sikorska-Nowak, Aneta. "The Henstock-Kurzweil-Pettis integrals and existence theorems for the Cauchy problem." Czechoslovak Mathematical Journal 54.2 (2004): 279-289. <http://eudml.org/doc/30859>.

@article{Cichoń2004,
abstract = {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.},
author = {Cichoń, Mieczysław, Kubiaczyk, Ireneusz, Sikorska-Nowak, Aneta, Sikorska-Nowak, Aneta},
journal = {Czechoslovak Mathematical Journal},
keywords = {pseudo-solution; Pettis integral; Henstock-Kurzweil integral; Cauchy problem; pseudo-solution; Pettis integral; Henstock-Kurzweil integral},
language = {eng},
number = {2},
pages = {279-289},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The Henstock-Kurzweil-Pettis integrals and existence theorems for the Cauchy problem},
url = {http://eudml.org/doc/30859},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Cichoń, Mieczysław
AU - Kubiaczyk, Ireneusz
AU - Sikorska-Nowak, Aneta, Sikorska-Nowak, Aneta
TI - The Henstock-Kurzweil-Pettis integrals and existence theorems for the Cauchy problem
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 2
SP - 279
EP - 289
AB - 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.
LA - eng
KW - pseudo-solution; Pettis integral; Henstock-Kurzweil integral; Cauchy problem; pseudo-solution; Pettis integral; Henstock-Kurzweil integral
UR - http://eudml.org/doc/30859
ER -

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