Asymptotic proximity to higher order nonlinear differential
equations

J 2022

Asymptotic proximity to higher order nonlinear differential equations

ASTASHOVA, Irina; Miroslav BARTUŠEK; Zuzana DOŠLÁ and Mauro MARINI

Basic information

Original name

Asymptotic proximity to higher order nonlinear differential equations

Authors

ASTASHOVA, Irina; Miroslav BARTUŠEK (203 Czech Republic, belonging to the institution); Zuzana DOŠLÁ (203 Czech Republic, guarantor, belonging to the institution) and Mauro MARINI

Edition

Advances in Nonlinear Analysis, Berlin, Walter de Gruyter GmbH, 2022, 2191-9496

Other information

Language

English

Type of outcome

Article in a journal

Field of Study

10101 Pure mathematics

Country of publisher

Germany

Confidentiality degree

is not subject to a state or trade secret

References:

URL

Impact factor

Impact factor: 4.200

RIV identification code

RIV/00216224:14310/22:00129115

Organization unit

Faculty of Science

DOI

https://doi.org/10.1515/anona-2022-0254

UT WoS

000811188400001

EID Scopus

2-s2.0-85132319202

Keywords in English

higher order differential equation; unbounded solutions; nonoscillatory solution; asymptotic behavior; topological methods

Abstract

In the original language

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.

Links

GA20-11846S, research and development project

Name: Diferenciální a diferenční rovnice reálných řádů: kvalitativní analýza a její aplikace

Investor: Czech Science Foundation

Cite

ASTASHOVA, Irina; Miroslav BARTUŠEK; Zuzana DOŠLÁ and Mauro MARINI. Asymptotic proximity to higher order nonlinear differential equations. Advances in Nonlinear Analysis. Berlin: Walter de Gruyter GmbH, 2022, vol. 11, No 1, p. 1598-1613. ISSN 2191-9496. Available from: https://doi.org/10.1515/anona-2022-0254.

@article{1874681,
   author = {Astashova, Irina and Bartušek, Miroslav and Došlá, Zuzana and Marini, Mauro},
   article_location = {Berlin},
   article_number = {1},
   doi = {https://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 and Mauro MARINI. Asymptotic proximity to higher order nonlinear differential equations. \textit{Advances in Nonlinear Analysis}. Berlin: Walter de Gruyter GmbH, 2022, vol.~11, No~1, p.~1598-1613. ISSN~2191-9496. Available from: https://doi.org/10.1515/anona-2022-0254.

Přehled o publikaci