02. Mamedova TF, Yegorova DK, Desyayev YeV, Hess R. Asymptotic integration of differential equations of Emden-Fowler

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UDC 517.9

DOI: 10.15507/0236-2910.026.201604.440-447

ASYMPTOTIC INTEGRATION OF DIFFERENTIAL EQUATIONS OF EMDEN-FOWLER

Tatyana F. Mamedova
professor of Applied Mathematics, Differential Equations and Theoretical Mechanics chair, National Research Mordovia State University (68, Bolshevistskaya St., Saransk, Russia), Ph.D. (Physics and Mathematics), docent, ORCID: http://orcid.org/0000-0002-7582-216X, This email address is being protected from spambots. You need JavaScript enabled to view it.

Darya K. Yegorova
docent of Applied Mathematics, Differential Equations and Theoretical Mechanics chair, National Research Mordovia State University, (68, Bolshevistskaya St., Saransk, Russia), Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0002-3392-6761, This email address is being protected from spambots. You need JavaScript enabled to view it.

Yevgeniy V. Desyayev
docent of Applied Mathematics, Differential Equations and Theoretical Mecha-nics chair, National Research Mordovia State University, (68, Bolshevistskaya St., Saransk, Russia), Ph.D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0003-2583-6966, This email address is being protected from spambots. You need JavaScript enabled to view it.

Ramin Hess
master of Economical faculty, University of Goettingen (1, Wilhelmplatz, Goettingen, Germany), ORCID: http://orcid.org/0000-0002-6347-9528, This email address is being protected from spambots. You need JavaScript enabled to view it.

Introduction: This article examines a new approach to the analysis of Emden-Fowler equations.
Materials and Methods: In this article, which is based on the methods proposed by V. Ye. Voskresensky [Comparison methods in nonlinear analysis? Saransk, 1990], a new approach to the analysis of Emden-Fowler equations was found. The concept of asymptotic equivalence of the differential equations has no unequivocal meaning. Various authors have different views on it. Nevertheless, all authors discuss about the equivalence relation defined by the asymptotic properties of the solutions. In general, this ratio is determined by the transformation semigroup with identity of a certain class of differential equations into itself.
Results: The paper contains asymptotic formula for the solution of nonlinear differential equations. The procedure outlined is required to solve the problem of the theorem and their implications. Also a complete proof of these theorems was conducted. These studies obtained more accurate formula for the solution of the equation of Emden-Fowler.
Discussion and Conclusions: The obtained results are consistent with similar studies of other authors and complement them. Further work on this topic involves the use of the results in a variety of applications, namely an application to the study of mathematical models in the field of economy and ecology.

Keywords: Emden-Fowler equation, asymptotic integration, asymptotic equivalence, differential equations, mathematical model

For citation: Mamedova TF, Yegorova DK, Desyayev YeV, Hess R. Asymptotic integration of differential equations of Emden-Fowler. Vestnik Mordovskogo universiteta = Mordovia University Bulletin. 2016; 4(26):440-447. DOI: 10.15507/0236-2910.026.201604.440-447

Acknowledgments: The authors express their appreciation and gratitude to the anonymous reviewer of the journal, whose detailed comments and recommendations helped to improve the article.

This work is licensed under a Creative Commons Attribution 4.0 License.