Vestnik of Samara University. Natural Science SeriesVestnik of Samara University. Natural Science Series2541-75252712-8954Samara National Research University447910.18287/2541-7525-2015-21-6-130-134ON ASYMPTOTIC PROPERTIES OF SOLUTIONS, DEFINED ON THE HALF OF AXIS OF ONE SEMILINEAR ODEFilimonovaI.V.morenov.sv@ssau.ruKhachlaevT.S.morenov.sv@ssau.ruLomonosov Moscow State UniversityMoscow State Institute of Radio Engineering, Electronics and Automation170620152161301341705201717052017Copyright © 2015, Filimonova I., Khachlaev T.2015The paper deals with the solutions of ordinary diﬀerential semi-linear equa- tion, the coeﬃcients of which depend on several real parameters. If the coeﬃcient is chosen so that the equation does not contain the ﬁrst-order derivative of the unknown function, it will be the case of Emden - Fowler equation. Asymp- totic behavior of Emden - Fowler equation solutions at inﬁnity is described in the book of Richard Bellman. The equations with the ﬁrst-order derivative, considered in this work, erase in some problems for elliptic partial diﬀerential equations in unbounded domains. The sign of the coeﬃcient in ﬁrst-order deriva- tive term essentially inﬂuences on the description of solutions. Partly the result of this paper can be obtained from the works of I.T. Kiguradze. In present work we use lemmas about the behavior of solutions of the linear equations with a strongly (weakly) increasing potential. The paper deals with the solutions of ordinary diﬀerential semi-linear equa- tion, the coeﬃcients of which depend on several real parameters. If the coeﬃcient is chosen so that the equation does not contain the ﬁrst-order derivative of the unknown function, it will be the case of Emden - Fowler equation. Asymp- totic behavior of Emden - Fowler equation solutions at inﬁnity is described in the book of Richard Bellman. The equations with the ﬁrst-order derivative, considered in this work, erase in some problems for elliptic partial diﬀerential equations in unbounded domains. The sign of the coeﬃcient in ﬁrst-order deriva- tive term essentially inﬂuences on the description of solutions. Partly the result of this paper can be obtained from the works of I.T. Kiguradze. In present work we use lemmas about the behavior of solutions of the linear equations with a strongly (weakly) increasing potential.обыкновенные дифференциальные уравнениянелинейные уравненияполулинейные уравненияуравнения Эмдена - Фаулераасимптотика решенийположительные решениясуществование решенийпринцип максимумаordinary differential equations, nonlinear equations, semilinear equations, Emden — Fowler equation, asymptotic behavior of solutions, positive solutions, existence of solutions, maximum principle