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De Haan type increasing solutions of half-linear differential equations

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ŘEHÁK Pavel

Druh Článek v odborném periodiku
Časopis / Zdroj J. Math. Anal. Appl.
Fakulta / Pracoviště MU

Pedagogická fakulta

Citace
Doi http://dx.doi.org/10.1016/j.jmaa.2013.10.048
Obor Obecná matematika
Klíčová slova Half-linear equation; increasing solution; Beurling slowly varying function; class Gamma; regular variation; rapid variation
Popis We study asymptotic behavior of eventually positive increasing solutions to the half-linear equation $(r(t)|y'|^{\alpha-1}\sgn y')'=p(t)|y|^{\alpha-1}\sgn y$, where $r,p$ are positive continuous functions and $\alpha\in(1,\infty)$. We give conditions which guarantee that any such a solution is in the class $\Gamma$ (in the de Haan sense). We also discuss regularly varying solutions and connections with a generalized regular variation and other related concepts. The results can be viewed as a half-linear extension of existing statements for linear equations, but in some aspects they are new also in the linear case.
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