Geodesic
On one method of studying implicit singular differential inclusions
Vestnik rossijskih universitetov. Matematika, Tome 22 (2017) no. 6, pp. 1314-1320

Voir la notice de l'article provenant de la source Math-Net.Ru

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, covering multi-valued mapping, Lipschitz multi-valued mapping.
Mots-clés : existence of solution 
@article{VTAMU_2017_22_6_a13,
     author = {E. A. Pluzhnikova and A. I. Shindyapin},
     title = {On one method of studying implicit singular differential inclusions},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {1314--1320},
     publisher = {mathdoc},
     volume = {22},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2017_22_6_a13/}
}
TY  - JOUR
AU  - E. A. Pluzhnikova
AU  - A. I. Shindyapin
TI  - On one method of studying implicit singular differential inclusions
JO  - Vestnik rossijskih universitetov. Matematika
PY  - 2017
SP  - 1314
EP  - 1320
VL  - 22
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VTAMU_2017_22_6_a13/
LA  - ru
ID  - VTAMU_2017_22_6_a13
ER  - 
%0 Journal Article
%A E. A. Pluzhnikova
%A A. I. Shindyapin
%T On one method of studying implicit singular differential inclusions
%J Vestnik rossijskih universitetov. Matematika
%D 2017
%P 1314-1320
%V 22
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VTAMU_2017_22_6_a13/
%G ru
%F VTAMU_2017_22_6_a13
E. A. Pluzhnikova; A. I. Shindyapin. On one method of studying implicit singular differential inclusions. Vestnik rossijskih universitetov. Matematika, Tome 22 (2017) no. 6, pp. 1314-1320. http://geodesic.mathdoc.fr/item/VTAMU_2017_22_6_a13/