Non-oscillation of modified Euler type linear and half-linear differential equations

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Publikace nespadá pod Filozofickou fakultu, ale pod Přírodovědeckou fakultu. Oficiální stránka publikace je na webu muni.cz.
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ŠIŠOLÁKOVÁ Jiřina

Rok publikování 2022
Druh Článek v odborném periodiku
Časopis / Zdroj European Journal of Mathematics
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www https://link.springer.com/article/10.1007/s40879-021-00522-4
Doi http://dx.doi.org/10.1007/s40879-021-00522-4
Klíčová slova Half-linear equation; Linear equation; Non-oscillation; Oscillation theory; Prüfer angle; Riccati equation
Popis Modified Euler type second order half-linear differential equations are considered and a non-oscillation criterion is derived for them. This criterion is the counterpart of a previously obtained oscillation theorem. Thus, from the main result of this paper, it follows that the studied equations are conditionally oscillatory in a very general case. To prove the non-oscillation criterion, a combination of the Riccati technique and the generalized Prüfer angle is used. Since the criterion is new in many cases (especially, in the linear case), several corollaries are formulated and the novelty is illustrated by an example as well.
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