Nonlinear Poincare-Perron theorem
Result description
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.
Keywords
Poincare-Perron theoremAsymptotic behaviorHalf-linear equation
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Nonlinear Poincare-Perron theorem
Original language description
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.
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
APPLIED MATHEMATICS LETTERS
ISSN
0893-9659
e-ISSN
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Volume of the periodical
121
Issue of the periodical within the volume
107425
Country of publishing house
US - UNITED STATES
Number of pages
7
Pages from-to
1-7
UT code for WoS article
000682955100024
EID of the result in the Scopus database
2-s2.0-85110370634
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Pure mathematics
Year of implementation
2021