Nonlinear Poincare-Perron theorem

被引：4
作者：
Rehak, Pavel [1 ]
机构：
[1] Brno Univ Technol, Inst Math, FME, Brno, Czech Republic
来源：
APPLIED MATHEMATICS LETTERS | 2021年 / 121卷
关键词：
Poincare-Perron theorem; Asymptotic behavior; Half-linear equation; EQUATIONS;
D O I：
10.1016/j.aml.2021.107425
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We establish a nonlinear extension of the Poincare-Perron theorem for a second order half-linear differential equation. Conditions are established which guarantee that all nontrivial solutions y of the equation are such that a proper limit lim(t ->infinity)y'(t)/y(t) exists. In addition, we discuss establishing precise asymptotic formulae for these solutions. We employ theory of regular variation and thereby, as a by-product, we complete some results for asymptotics of differential equations considered in this framework. The results can serve for comparison purposes involving more general equations and are of importance also from the stability point of view. (C) 2021 Elsevier Ltd. All rights reserved.
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页数：7
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