Asymptotic integration of differential equations of Emden-Fowler

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.