Differential inclusions and multivalued integrals

Kinga Cichoń; Mieczysław Cichoń; Bianca Satco

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2013)

  • Volume: 33, Issue: 2, page 171-191
  • ISSN: 1509-9407

Abstract

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In this paper we consider the nonlocal (nonstandard) Cauchy problem for differential inclusions in Banach spaces x'(t) ∈ F(t,x(t)), x(0)=g(x), t ∈ [0,T] = I. Investigation over some multivalued integrals allow us to prove the existence of solutions for considered problem. We concentrate on the problems for which the assumptions are expressed in terms of the weak topology in a Banach space. We recall and improve earlier papers of this type. The paper is complemented by a short survey about multivalued integration including Pettis and Henstock-Kurzweil-Pettis multivalued integrals.

How to cite

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Kinga Cichoń, Mieczysław Cichoń, and Bianca Satco. "Differential inclusions and multivalued integrals." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 33.2 (2013): 171-191. <http://eudml.org/doc/270414>.

@article{KingaCichoń2013,
abstract = { In this paper we consider the nonlocal (nonstandard) Cauchy problem for differential inclusions in Banach spaces x'(t) ∈ F(t,x(t)), x(0)=g(x), t ∈ [0,T] = I. Investigation over some multivalued integrals allow us to prove the existence of solutions for considered problem. We concentrate on the problems for which the assumptions are expressed in terms of the weak topology in a Banach space. We recall and improve earlier papers of this type. The paper is complemented by a short survey about multivalued integration including Pettis and Henstock-Kurzweil-Pettis multivalued integrals. },
author = {Kinga Cichoń, Mieczysław Cichoń, Bianca Satco},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {nonlocal Cauchy problem; Aumann integrals; Pettis integrals; Henstock-Kurzweil-Pettis integrals; measure of weak noncompactness},
language = {eng},
number = {2},
pages = {171-191},
title = {Differential inclusions and multivalued integrals},
url = {http://eudml.org/doc/270414},
volume = {33},
year = {2013},
}

TY - JOUR
AU - Kinga Cichoń
AU - Mieczysław Cichoń
AU - Bianca Satco
TI - Differential inclusions and multivalued integrals
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2013
VL - 33
IS - 2
SP - 171
EP - 191
AB - In this paper we consider the nonlocal (nonstandard) Cauchy problem for differential inclusions in Banach spaces x'(t) ∈ F(t,x(t)), x(0)=g(x), t ∈ [0,T] = I. Investigation over some multivalued integrals allow us to prove the existence of solutions for considered problem. We concentrate on the problems for which the assumptions are expressed in terms of the weak topology in a Banach space. We recall and improve earlier papers of this type. The paper is complemented by a short survey about multivalued integration including Pettis and Henstock-Kurzweil-Pettis multivalued integrals.
LA - eng
KW - nonlocal Cauchy problem; Aumann integrals; Pettis integrals; Henstock-Kurzweil-Pettis integrals; measure of weak noncompactness
UR - http://eudml.org/doc/270414
ER -

References

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