INVESTIGATION OF SOME CLASSES OF SPECIAL SOLUTIONS OF ESSENTIALLY NONLINEAR SECOND ORDER DIFFERENTIAL EQUATIONS
Journal Title: Дослідження в математиці і механіці - Year 2018, Vol 23, Issue 2
Abstract
The sufficiently wide class of slowly varying solutions as the argument tends to the special point for essentially nonlinear second order differential equations is considered. The necessary and sufficient conditions of the existence of solutions of considered class are obtained. The asymptotic representations as the argument tends to a special point of such solutions and their first derivatives are found also. The results of the work can be used by the investigation of solutions on infinity and for singular solutions.
Authors and Affiliations
G. A. Gerzhanovskaya
Keywords
Related Articles
- EP ID EP558778
- DOI 10.18524/2519-206x.2018.2(32).149700
- Views 86
- Downloads 0
On the 80th anniversary of Victor Plotnikov
К 80-ЛЕТИЮ СО ДНЯ РОЖДЕНИЯ ВИКТОРА АЛЕКСАНДРОВИЧА ПЛОТНИКОВА 5 января 1938 г. — 4 сентября 2006 г.
Conditions of existence and uniqueness of solutions for set-valued Volterra integral equation
In 1969, F. S. de Blasi and F. Iervolino examined set-valued differential equation (differential equation with derivative Hukuhara). In the future, many authors have studied the question of the existence, uniqueness and...
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...
DISTRIBUTION OF THE WEIGHTS OF THE KLOOSTERMAN CODE
Tran The Vinh. Distribution of the weights of the Kloosterman code. Studied 𝑝-ary Kloosterman codes of length 𝑝2 − 1 in alphabet F𝑞 which are the cyclic codes of the dual Melas code of length 𝑝2 − 1. We obtain the weight...
On exponential sums involving the divisor function over Z[𝑖]
We apply the van der Corput transform to investigate the sums of view Σ︀ 𝑟(𝑛)𝑔(𝑛)𝑒(𝑓(𝑛))), where 𝑟(𝑛) is the number of representations of 𝑛 as the sum of two squares of integer numbers. Such sums have been studied by M....