Vladikavkazskii Matematicheskii Zhurnal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vladikavkaz. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Vladikavkazskii Matematicheskii Zhurnal, 2022, Volume 24, Number 1, Pages 54–64
DOI: https://doi.org/10.46698/p7919-5616-0187-g
(Mi vmj801)
 

Existence and uniqueness theorems for a differential equation with a discontinuous right-hand side

M. G. Magomed-Kasumov

Southern Mathematical Institute VSC RAS, 53 Vatutin St., Vladikavkaz 362027, Russia
References:
Abstract: We consider new conditions for existence and uniqueness of a Caratheodory solution for an initial value problem with a discontinuous right-hand side. The method used here is based on: 1) the representation of the solution as a Fourier series in a system of functions orthogonal in Sobolev sense and generated by a classical orthogonal system; 2) the use of a specially constructed operator $A$ acting in $l_2$, the fixed point of which are the coefficients of the Fourier series of the solution. Under conditions given here the operator $A$ is contractive. This property can be employed to construct robust, fast and easy to implement spectral numerical methods of solving an initial value problem with discontinuous right-hand side. Relationship of new conditions with classical ones (Caratheodory conditions with Lipschitz condition) is also studied. Namely, we show that if in classical conditions we replace $L^1$ by $L^2$, then they become equivalent to the conditions given in this article.
Key words: initial value problem, Cauchy problem, discontinuous right-hand side, Sobolev orthogonal system, existence and uniqueness theorem, Caratheodory solution.
Received: 23.05.2021
Bibliographic databases:
Document Type: Article
UDC: 517.927.4
Language: English
Citation: M. G. Magomed-Kasumov, “Existence and uniqueness theorems for a differential equation with a discontinuous right-hand side”, Vladikavkaz. Mat. Zh., 24:1 (2022), 54–64
Citation in format AMSBIB
\Bibitem{Mag22}
\by M.~G.~Magomed-Kasumov
\paper Existence and uniqueness theorems for a differential equation with a discontinuous right-hand side
\jour Vladikavkaz. Mat. Zh.
\yr 2022
\vol 24
\issue 1
\pages 54--64
\mathnet{http://mi.mathnet.ru/vmj801}
\crossref{https://doi.org/10.46698/p7919-5616-0187-g}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4405956}
Linking options:
  • https://www.mathnet.ru/eng/vmj801
  • https://www.mathnet.ru/eng/vmj/v24/i1/p54
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Владикавказский математический журнал
    Statistics & downloads:
    Abstract page:114
    Full-text PDF :43
    References:23
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025