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Filippov solutions of vector Dirichlet problems

  • Hana Machů EMAIL logo
Veröffentlicht/Copyright: 10. März 2020
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Abstract

If in the right-hand sides of given differential equations occur discontinuities in the state variables, then the natural notion of a solution is the one in the sense of Filippov. In our paper, we will consider this type of solutions for vector Dirichlet problems. The obtained theorems deal with the existence and localization of Filippov solutions, under effective growth restrictions. Two illustrative examples are supplied.

MSC 2010: 34A60; 34B15; 34B16; 34B27; 47H04
  1. (Communicated by Michal Fečkan )

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Received: 2019-05-30
Accepted: 2019-08-01
Published Online: 2020-03-10
Published in Print: 2020-04-28

© 2020 Mathematical Institute Slovak Academy of Sciences

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