0470375 - MÚ 2017 RIV SK eng J - Journal Article
Řehák, Pavel
A few remarks on Poincare-Perron solutions and regularly varying solutions.
Mathematica Slovaca. Roč. 66, č. 6 (2016), s. 1297-1318. ISSN 0139-9918. E-ISSN 1337-2211
Institutional support: RVO:67985840
Keywords : Perron theorem * regularly varying solution * linear differential equation
OECD category: Pure mathematics
Impact factor: 0.346, year: 2016
https://www.degruyter.com/view/j/ms.2016.66.issue-6/ms-2016-0224/ms-2016-0224.xml?format=INT

We establish conditions guaranteeing the existence of (generalized) regularly varying solutions to $n$-th order linear differential and $q$-difference equations. The proofs are based mainly on classical Poincar'e's and Perron's theorems and certain transformations. In some special cases, our results reduce to the existing ones, thus actually we offer an alternative approach to some parts of the asymptotic theory of differential equations made in the framework of regular variation. For higher order cases, our statements are essentially new. Another important feature of this paper is that it reveals connections among various results and somehow revises some of them.
Permanent Link: http://hdl.handle.net/11104/0268033