Asymptotic proximity to higher order nonlinear differential equations

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Publikace nespadá pod Pedagogickou fakultu, ale pod Přírodovědeckou fakultu. Oficiální stránka publikace je na webu muni.cz.
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ASTASHOVA Irina BARTUŠEK Miroslav DOŠLÁ Zuzana MARINI Mauro

Rok publikování 2022
Druh Článek v odborném periodiku
Časopis / Zdroj Advances in Nonlinear Analysis
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www https://www.degruyter.com/document/doi/10.1515/anona-2022-0254/html
Doi http://dx.doi.org/10.1515/anona-2022-0254
Klíčová slova higher order differential equation; unbounded solutions; nonoscillatory solution; asymptotic behavior; topological methods
Popis 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.
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