Half-linear differential equations, the Karamata theory, and the de Haan theory

0485671 - MÚ 2018 RIV JP eng C - Konferenční příspěvek (zahraniční konf.)
Řehák, Pavel
Half-linear differential equations, the Karamata theory, and the de Haan theory.
Qualitative theory of ordinary differential equations in real domains. Kyoto: Research lnstitute for Mathematical Sciences, 2016 - (Yamaoka, N.), s. 1-25. RIMS Kokyuroku, 1993. ISSN 1880-2818.
[Qualitative theory of ordinary differential equations in real domains. Kyoto (JP), 09.11.2015-11.11.2015]
Institucionální podpora: RVO:67985840
Klíčová slova: differential equations * Karamata theory * Haan theory
Obor OECD: Pure mathematics
http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1993-01.pdf

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.
Trvalý link: http://hdl.handle.net/11104/0280632