Asymptotic equivalence relations for rapidly varying solutions of sublinear differential equations of Emden–Fowler type

We discuss sublinear differential equations of the Emden–Fowler type x ″ = q ( t ) x γ under the assumption that the coefficient q is a rapidly varying function. We show that all of their strongly decreasing and strongly increasing solutions are rapidly varying functions and are in the asymptotic eq...

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Bibliographic Details
Published in:Advances in continuous and discrete models 2022-03, Vol.2022 (1), Article 19
Main Authors: Manojlović, Jelena, Milošević, Jelena
Format: Article
Language:English
Subjects:
Analysis
Asymptotic properties
Difference and Functional Equations
Differential equations
Equivalence
Functional Analysis
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
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Summary:We discuss sublinear differential equations of the Emden–Fowler type x ″ = q ( t ) x γ under the assumption that the coefficient q is a rapidly varying function. We show that all of their strongly decreasing and strongly increasing solutions are rapidly varying functions and are in the asymptotic equivalence relation with a precisely defined function determined by the coefficient q .
ISSN:2731-4235
1687-1839
2731-4235
1687-1847
DOI:10.1186/s13662-022-03693-w