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@article{1874681,
author = {Astashova, Irina and Bartušek, Miroslav and Došlá, Zuzana and Marini, Mauro},
article_location = {Berlin},
article_number = {1},
doi = {http://dx.doi.org/10.1515/anona-2022-0254},
keywords = {higher order differential equation; unbounded solutions; nonoscillatory solution; asymptotic behavior; topological methods},
language = {eng},
issn = {2191-9496},
journal = {Advances in Nonlinear Analysis},
title = {Asymptotic proximity to higher order nonlinear differential equations},
url = {https://www.degruyter.com/document/doi/10.1515/anona-2022-0254/html},
volume = {11},
year = {2022}
}
TY - JOUR
ID - 1874681
AU - Astashova, Irina - Bartušek, Miroslav - Došlá, Zuzana - Marini, Mauro
PY - 2022
TI - Asymptotic proximity to higher order nonlinear differential equations
JF - Advances in Nonlinear Analysis
VL - 11
IS - 1
SP - 1598-1613
EP - 1598-1613
PB - Walter de Gruyter GmbH
SN - 21919496
KW - higher order differential equation
KW - unbounded solutions
KW - nonoscillatory solution
KW - asymptotic behavior
KW - topological methods
UR - https://www.degruyter.com/document/doi/10.1515/anona-2022-0254/html
N2 - The existence of unbounded solutions and their asymptotic behavior is studied for higher order differential equations considered as perturbations of certain linear differential equations. In particular, the existence of solutions with polynomial-like or noninteger power-law asymptotic behavior is proved. These results give a relation between solutions to nonlinear and corresponding linear equations, which can be interpreted, roughly speaking, as an asymptotic proximity between the linear case and the nonlinear one. Our approach is based on the induction method, an iterative process and suitable estimates for solutions to the linear equation.
ER -
ASTASHOVA, Irina, Miroslav BARTUŠEK, Zuzana DOŠLÁ a Mauro MARINI. Asymptotic proximity to higher order nonlinear differential equations. \textit{Advances in Nonlinear Analysis}. Berlin: Walter de Gruyter GmbH, 2022, roč.~11, č.~1, s.~1598-1613. ISSN~2191-9496. Dostupné z: https://dx.doi.org/10.1515/anona-2022-0254.
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