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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

On the General Solution to the Bratu and Generalized Bratu Equations

Lucas Hervé Koudahoun1, Jean Akande1, Damien Kêgnidé Kolawolé Adjaï1, Yélomè Judicaël Fernando Kpomahou2 and Marc Delphin Monsia1
  • 1 University of Abomey-Calavi, Benin
  • 2 University of Abomey, Benin

Abstract

This work shows that the Bratu equation belongs to a general class of Liénard-type equations for which the general solution may be exactly and explicitly computed within the framework of the generalized Sundman transformation. In this perspective the exact solution of the Bratu nonlinear two-point boundary value problem as well as of some well-known Bratu-type problems have been determined.

Journal of Mathematics and Statistics
Volume 14 No. 1, 2018, 193-200

DOI: https://doi.org/10.3844/jmssp.2018.193.200

Submitted On: 12 May 2018 Published On: 14 July 2018

How to Cite: Koudahoun, L. H., Akande, J., Kolawolé Adjaï, D. K., Kpomahou, Y. J. F. & Monsia, M. D. (2018). On the General Solution to the Bratu and Generalized Bratu Equations. Journal of Mathematics and Statistics, 14(1), 193-200. https://doi.org/10.3844/jmssp.2018.193.200

Open AccessCopyright: © 2018 Lucas Hervé Koudahoun, Jean Akande, Damien Kêgnidé Kolawolé Adjaï, Yélomè Judicaël Fernando Kpomahou and Marc Delphin Monsia. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Bratu Equation
  • Boundary Value Problem
  • Initial Value Problem
  • General Solution
  • Generalized Sundman Transformation