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ArticleOriginal scientific text

Title

Differential inclusions and multivalued integrals

Authors 1, 2, 3

Affiliations

  1. Institute of Mathematics, Faculty of Electrical Engineering, Poznań University of Technology, Piotrowo 3a, 60-965 Poznań, Poland
  2. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
  3. "Stefan cel Mare" University of Suceava, Faculty of Electrical Engineering and Computer Science, Universitatii 13, Suceava, Romania

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.

Keywords

ENG
nonlocal Cauchy problem, Aumann integrals, Pettis integrals, Henstock-Kurzweil-Pettis integrals, measure of weak noncompactness

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Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2013/33/2
Export to PBN, Opens in new tab
Pages:
171-191
Main language of publication
English
Received
2013-06-20
Published
2013

DOI: 10.7151/dmdico1147

Exact and natural sciences