Araştırma Makalesi

On the integration of first order nonlinear differential equations and the conditions of Fuchs' theorem

Cilt: 6 Sayı: 3 30 Eylül 2022
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On the integration of first order nonlinear differential equations and the conditions of Fuchs' theorem

Öz

In this paper we give the general solutions of a class of first order nonlinear Fuchs ordinary differential equations. This leads us to show by an example that the necessary conditions of Fuchs' theorem are not sufficient.

Anahtar Kelimeler

Kaynakça

  1. [1] F.J. Bureau, differential equations with fixed critical points. Annali di Matematica pura ed applicata, 1964, LXIV, 229-364.
  2. [2] R. Conte, The Painlevé approach to nonlinear ordinary differential equations, The Painlevé Property, Springer-Verlag, New York 1999, 77-180.
  3. [3] R. Conte, Unification of PDE and ODE versions of Painlevé analysis into a single invariant version, Painlevé transcendents, their asymptotics and physical applications, eds. D. Levi and P. Winternitz, Plenum, New York, 1992, 125-144.
  4. [4] R. Conte et al., Direct and inverse methods in nonlinear evolution equations. Springer-Verlag, Berlin 2003.
  5. [5] L. Fuchs,über differentialgleichungen, deren integrale feste verzweigungspunkte besitzen. Koniglichen Preussischen Akademie der Wissenschaften, 1884, 32, 699-719.
  6. [6] V.V. Golubev, Lectures on Analytic Theory of Differential Equations [in Russian], Gostekhteorizdat, Moscow, 1950. [7] C. Hermite, Course Lithographie de l'Ecole Polytechnique, Paris, 1873.
  7. [8] E. Hille, Ordinary Differential Equations in the Complex Domai. Wiley-Interscience, New York, 1976.
  8. [9] E. L. Ince, Ordinary Di?erential Equations. Dover, New york, 1964.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Matematik

Bölüm

Araştırma Makalesi

Yayımlanma Tarihi

30 Eylül 2022

Gönderilme Tarihi

18 Ocak 2022

Kabul Tarihi

18 Nisan 2022

Yayımlandığı Sayı

Yıl 2022 Cilt: 6 Sayı: 3

Kaynak Göster

APA
Kessi, A., Laadj, T., & Yahi, M. (2022). On the integration of first order nonlinear differential equations and the conditions of Fuchs’ theorem. Advances in the Theory of Nonlinear Analysis and its Application, 6(3), 347-353. https://doi.org/10.31197/atnaa.1059343
AMA
1.Kessi A, Laadj T, Yahi M. On the integration of first order nonlinear differential equations and the conditions of Fuchs’ theorem. ATNAA. 2022;6(3):347-353. doi:10.31197/atnaa.1059343
Chicago
Kessi, Arezki, Toufik Laadj, ve Moussa Yahi. 2022. “On the integration of first order nonlinear differential equations and the conditions of Fuchs’ theorem”. Advances in the Theory of Nonlinear Analysis and its Application 6 (3): 347-53. https://doi.org/10.31197/atnaa.1059343.
EndNote
Kessi A, Laadj T, Yahi M (01 Eylül 2022) On the integration of first order nonlinear differential equations and the conditions of Fuchs’ theorem. Advances in the Theory of Nonlinear Analysis and its Application 6 3 347–353.
IEEE
[1]A. Kessi, T. Laadj, ve M. Yahi, “On the integration of first order nonlinear differential equations and the conditions of Fuchs’ theorem”, ATNAA, c. 6, sy 3, ss. 347–353, Eyl. 2022, doi: 10.31197/atnaa.1059343.
ISNAD
Kessi, Arezki - Laadj, Toufik - Yahi, Moussa. “On the integration of first order nonlinear differential equations and the conditions of Fuchs’ theorem”. Advances in the Theory of Nonlinear Analysis and its Application 6/3 (01 Eylül 2022): 347-353. https://doi.org/10.31197/atnaa.1059343.
JAMA
1.Kessi A, Laadj T, Yahi M. On the integration of first order nonlinear differential equations and the conditions of Fuchs’ theorem. ATNAA. 2022;6:347–353.
MLA
Kessi, Arezki, vd. “On the integration of first order nonlinear differential equations and the conditions of Fuchs’ theorem”. Advances in the Theory of Nonlinear Analysis and its Application, c. 6, sy 3, Eylül 2022, ss. 347-53, doi:10.31197/atnaa.1059343.
Vancouver
1.Arezki Kessi, Toufik Laadj, Moussa Yahi. On the integration of first order nonlinear differential equations and the conditions of Fuchs’ theorem. ATNAA. 01 Eylül 2022;6(3):347-53. doi:10.31197/atnaa.1059343