
Conditions for the existence and asymptotic of a class of solutions of essential
nonlinear differential equations of the second order (in Russian) 
Author 
À. A. Kozma
sanjakos@ukr.net
Îäåññêèé ãîñóäàðñòâåííûé ýêîíîìè÷åñêèé óíèâåðñèòåò

Abstract 
We consider the ordinary differential equation of the second order containing in the righthand
side the sum of nonlinearities correctly varying concerning unknown function and its
derivative of the first order. Necessary and sufficient conditions of existence of a wide class of
monotone solutions, and exact asymptotic representations of solutions from the given class in
a neighborhood of a singular point are established. 
Keywords 
differential equation; asymptotic representation of solution 
Reference 
1. Belozerova M.A. Asymptotic properties of a class of solutions of essential nonlinear differential equations
of the second order// Mat. Stud. – 2008. – V.29, ¹1. – P. 52–62. (in Ukrainian)
2. Belozerova M.A. Asymptotic representations of solutions of a nonautonomous second order differential
equations with close to powertype nonlinearities. // Nonlinear Oscilations. – 2009. – V.12, ¹1. – P. 3–15.
(in Russian)
3. Kasianova V.A. Asymptotical representations of the disappearing solutions of sufficiently nonlinear differential
equations of the second order// Nauk. Visn. Chernivets’kogo Univ. Mat. – 2004. – V.228. – P.
5–19. (in Ukrainian)
4. Evtukhov V.M., Kas’yanova V.A. Asymptotic behavior of unbounded solutions of essentially nonlinear
secondorder differential equations. I.// Ukr. Mat. Zh. – 2005. – V.57, ¹3. – P. 338–355. (in Russian)
5. Kozma A.A. Asymptotic representations of a certain class of solutions of essentially nonlinear second
order differential equations// Nonlinear Oscilations. – 2006. – V.9, ¹4. – P. 490–501. (in Russian)
6. Kozma A.A. Asymptotic behavior of solutions of essentially nonlinear differential equations of the second
order// Nauk. Visn. Chernivets’kogo Univ. Mat. – 2008. – V.374. – P. 55–65. (in Ukrainian)
7. Kozma A.A. Existence conditions for one class solutions of secondorder nonlinear differential equations//
Bulletin of the Odessa National University. Mathematics and mechanics. – 2009. – V.14, ¹20. – P. 75–90.
(in Russian)
8. Evtukhov V.M., Samoilenko A.M. Conditions for the existence of solutions of real nonautonomous systems
of quasilinear differential equations vanishing at a singular point// Ukr. Mat. Zh. – 2010. – V.62, ¹1. –
P. 52–80. (in Russian)

Pages 
176187 
Volume 
36 
Issue 
2 
Year 
2011 
Journal 
Matematychni Studii 
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