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A few remarks on Poincare-Perron solutions and regularly varying solutions
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SYSNO ASEP 0470375 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title A few remarks on Poincare-Perron solutions and regularly varying solutions Author(s) Řehák, Pavel (MU-W) RID, SAI, ORCID Source Title Mathematica Slovaca. - : Walter de Gruyter - ISSN 0139-9918
Roč. 66, č. 6 (2016), s. 1297-1318Number of pages 22 s. Language eng - English Country SK - Slovakia Keywords Perron theorem ; regularly varying solution ; linear differential equation Subject RIV BA - General Mathematics OECD category Pure mathematics Institutional support MU-W - RVO:67985840 UT WOS 000398461200004 EID SCOPUS 85014671312 DOI https://doi.org/10.1515/ms-2016-0224 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2017
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