Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Canonical Duality-Triality Theory: Unified Understanding for Modeling, Problems, and NP-Hardness in Global Optimization of Multi-Scale Systems Read chapter Read first chapter

2019 | OriginalPaper | Chapter

The Properties of Certain Linear and Nonlinear Differential Equations

Authors : Galina Filipuk, Alexander Chichurin

Published in: Advances in Mathematical Methods and High Performance Computing

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We consider linear differential equations of the second- and the third-order and nonlinear second-order differential equations related via the Schwarzian derivative. The main objective of the paper is to obtain relations between the solutions of the second- and the third-order linear differential equations and the solutions of the nonlinear differential equations of the second order. The method is based on the use of the Schwarzian derivative, which is defined as the ratio of two linearly independent solutions of the linear differential equations of the second and the third order. As a result, we obtain new relations between the solutions of these linear and nonlinear equations.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Modified Post-Widder Operators Preserving Exponential Functions
next chapter Fixed Points for (ϕ, ψ)-Contractions in Menger Probabilistic Metric Spaces
Literature
1.
Ahlfors, L. V.: Möbius transformations in several dimensions. Lecture notes at the University of Minnesota, Minneapolis (1981)MATH
2.
Dobrovolsky, V.A.: Essays on the development of the analytic theory of differential equations. Vishcha Shkola, Kiev (1974) (in Russian)
3.
4.
Lukashevich, N. A., Martynov, I. P.: On the third order linear equations. Materials of the International Scientific Conference ”Differential Equations and Their Applications”, Grodno, Grodno State University, 78–85 (1998) (in Russian)
5.
Lukashevich, N. A., Chichurin, A.V.: Differential equations of the first order. Belarusian State University, Minsk (1999) (in Russian)MATH
6.
Ince, E. L.: Ordinary differential equations. Dover Publications, New York (1956)
7.
Chichurin, A.V.: The Chazy equation and linear equations of the Fuchs class. Publ. RUDN, Moscow (2003) (in Russian)
8.
Chichurin, A., Stepaniuk G.: The computer method of construction of the general solution of the linear differential equation of the third order. Studia i Materialy EWSIE, 8, 17–27 (2014)
9.
Chichurin, A.V., Stepaniuk, G.P.: General solution to the fourth order linear differential equation with coefficients satisfying the system of three first order differential equations. Bulletin of Taras Shevchenko National University of Kyiv, Series: Physics & Mathematics, 31, No.1, 29–34 (2014)
10.
Chichurin, A.V.: The computer method of construction of the general solution of the nonlinear differential equation of the fourth order. Studia i Materialy EWSIE, 7, 39–47 (2014)
11.
Chichurin, A.: Computer construction of the general solution of the linear differential equation of the fifth order. Recent Developments in Mathematics and Informatics, Vol. I. Contemporary Mathematics and Computer Science, KUL, Lublin, 19-36 (2016)
Metadata
Title
The Properties of Certain Linear and Nonlinear Differential Equations
Authors
Galina Filipuk
Alexander Chichurin
Copyright Year
2019
Book
Advances in Mathematical Methods and High Performance Computing

Print ISBN: 978-3-030-02486-4

Electronic ISBN: 978-3-030-02487-1

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-02487-1_11

Premium Partner

    Image Credits