Loading [MathJax]/jax/output/CommonHTML/jax.js
Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.:
Year:
Volume:
Issue:
Page:
Find




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

Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2024, Volume 233, Pages 99–106
DOI: https://doi.org/10.36535/2782-4438-2024-233-99-106 (Mi into1282) 		 
Branching equation for a first-order differential equation in a Banach space with quadratic perturbations of a small parameter

V. I. Uskov

Voronezh State University of Forestry and Technologies named after G.F. Morozov
Full-text PDF (281 kB)
References:
PDF
HTML
DOI: https://doi.org/10.36535/2782-4438-2024-233-99-106
Abstract: This paper is devoted to the study of the behavior as ε→0 of solutions of the Cauchy problem for a first-order differential equation in a Banach space with quadratic operator pencils with the derivative of the unknown function. The branching equation is obtained and analyzed by using the Newton diagram. The conditions of the appearing of a boundary layer near the initial point are identified and the structure of boundary-layer functions is determined.
Keywords: branching equation, first-order differential equation, Fredholm operator, Banach space, quadratic perturbation, small parameter, boundary layer
Document Type: Article
UDC: 517.928
MSC: 34E15
Language: Russian
Citation: V. I. Uskov, “Branching equation for a first-order differential equation in a Banach space with quadratic perturbations of a small parameter”, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 4, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 233, VINITI, Moscow, 2024, 99–106
Citation in format AMSBIB
\Bibitem{Usk24}
\by V.~I.~Uskov
\paper Branching equation for a first-order differential equation in a Banach space with quadratic perturbations of a small parameter
\inbook Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 4
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2024
\vol 233
\pages 99--106
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1282}
\crossref{https://doi.org/10.36535/2782-4438-2024-233-99-106}
Linking options:
  • https://www.mathnet.ru/eng/into1282
  • https://www.mathnet.ru/eng/into/v233/p99
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
    Statistics & downloads:
    Abstract page:70
    Full-text PDF :17
    References:20
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025