This article is cited in 1 paper

MATHEMATICS

On one method of studying implicit singular differential inclusions

E. A. Pluzhnikova^ab, A. I. Shindyapin<sup>c

a</sup> Tambov State University named after G.R. Derzhavin
^b RUDN University
^c Universidade Eduardo Mondlane

Abstract: We propose a method of studying singular differential inclusions based on the representation of such an inclusion in the form of an operator inclusion in some space of measurable functions depending on the type of a given singularity. To the operator inclusion we apply the results on Lipschitz perturbations of multi-valued covering mappings.
The article consists of three sections. In the first one we give the necessary definitions and formulate the theorem [A. Arutyunov, V.A. de Oliveira, F.L. Pereira, E. Zhukovskiy, S. Zhukovskiy // Applicable Analysis, 2015, 94, № 1] on the Lipschitz perturbations of multi-valued covering mappings. In the second section we introduce special metric spaces of integrable functions and obtain sufficient conditions of covering for the multi-valued Nemytskii operator in such spaces. Finally, using the mentioned results, we derive the existence conditions for the Cauchy problem for an implicit singular differential inclusion.

Keywords: implicit singular differential inclusion, Cauchy problem, existence of solution, covering multi-valued mapping, Lipschitz multi-valued mapping.

UDC: 517.988.6, 517.922

Received: 09.09.2017

DOI: 10.20310/1810-0198-2017-22-6-1314-1320