Asymptotics of one class of solutions of 𝑛-th order ordinary differential equations with regularly varying nonlinearities
Journal Title: Дослідження в математиці і механіці - Year 2017, Vol 22, Issue 2
Abstract
In the present paper the existence conditions of solutions, for each of which there exists a number 𝑘 P t3, . . . , 𝑛u such that p𝑛 _ 𝑘q-th derivative of solution tends to nonzero constant as the argument tends to 8, of a binomial non-autonomous 𝑛-th order ordinary differential equation with regularly varying nonlinearities and the asymptotic representations of their derivatives of order up to 𝑛_1 are established. During the investigation of this question the problems with the asymptotics of p𝑛_𝑘1q–st and the subsequent derivatives of order ¤ 𝑛_1 are arose. As a result, the class of so-called 𝒫𝑘 8p𝜆0q–solutions, where _8 ¤ 𝜆0 ¤ 8, is introduced and the question of existence and asymptotics of 𝒫𝑘 8p𝜆0q–solutions in singular cases, when 𝜆0 _ 𝑛_𝑗_1 𝑛_𝑗 , 𝑗 _ 𝑛 _ 𝑘 2,𝑛 _ 1, is considered. All other nonsingular cases have been studied in the previous author’s works. These results are essentially complement the research concerning the existence of such solutions in the monograph by I. T. Kiguradze and T. A. Chanturiya for the equations of general type and the differential equations of Emden-Fauler type, where a considerably strict restriction to the p𝑛_𝑘1q-st derivative of solution is provided for.
Authors and Affiliations
K. S. Korepanova
Keywords
Related Articles
- EP ID EP343937
- DOI -
- Views 86
- Downloads 0
On some nonlocal boundary value problems for nonlinear ordinary differential equations with delay
The results of this paper were reported at International Workshop “Nonlinear Analysis and Nonautonomous Ordinary Differential Equations” (Odessa, Ukraine, June 23-27, 2017). In the paper, nonlocal boundary value problems...
DYNAMICS OF A STOCHASTIC LOTKA–VOLTERRA FOOD CHAIN MODEL
The authors would like to thank Nguyen Hai Dang for his comments on the manuscript of this paper. This paper is concerned with a stochastic Lotka-Volterra food chain model. The existence of the global solution and the ul...
Interfacial prefracture zone at the corner point of the media-seperating boundary
The symmetric problem on the calculation of a plastic prefracture zone at the corner point of the interface of two isotropic media is considered. The piece-homogeneous isotropic body with the media-separating boundary in...
ON THE MULTIPLICATIVE PARTITION FUNCTION
We study the number of representations n=s1⋯sm, where sj are sonor numbers, i.e. for every sj there do not exist the natural numbers n and k such that sj=nk, k⩾2. The counting function f(n) of such representation is the...
On a two-step algorithm in structural and parametric optimization problems of linear control systems.
This paper deals with applying of a two-step optimization algorithm for structural and parametric optimization problems of linear control systems with fixed and floating switching points.