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Differential inclusions and multivalued integrals

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