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Half-linear differential equations, the Karamata theory, and the de Haan theory
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SYSNO ASEP 0485671 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title Half-linear differential equations, the Karamata theory, and the de Haan theory Author(s) Řehák, Pavel (MU-W) RID, SAI, ORCID Source Title Qualitative theory of ordinary differential equations in real domains. - Kyoto : Research lnstitute for Mathematical Sciences, 2016 / Yamaoka N. - ISSN 1880-2818 Pages s. 1-25 Number of pages 25 s. Publication form Print - P Action Qualitative theory of ordinary differential equations in real domains Event date 09.11.2015 - 11.11.2015 VEvent location Kyoto Country JP - Japan Event type WRD Language eng - English Country JP - Japan Keywords differential equations ; Karamata theory ; Haan theory Subject RIV BA - General Mathematics OECD category Pure mathematics Institutional support MU-W - RVO:67985840 Annotation Our results can be understood in several ways. We solve open problems posed in the literature ([31, 34, 37]). We generalize results for linear differential equations ([6, 10, 23, 24, 25, 31]), many of our observations are new even in the linear case. We provide a refinement on information about behavior of solutions of (1) in standard asymptotic classes ([2, 3]). We describe behavior of regularly and rapidly varying solutions which are known to exist ([3, 12, 13, 31, 34]). We prove regular or rapid variation of all positive solutions. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2018
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