Naslov
Non-monotone positive solutions of second-order linear differential equations: existence, nonexistence and criteria

Autori
Pašić, Mervan ; Tanaka, Satoshi

Izvornik
Electronic Journal of Qualitative Theory of Differential Equations (1417-3875) 2016 (2016), 93; 1-25

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
non-monotonic behaviour ; positive solutions ; existence ; nonexistence ; criteria

Sažetak
We study non-monotone positive solutions of the second- order linear differential equations: $(p(t)x')' + q(t) x = e(t)$, with positive $p(t)$ and $q(t)$. For the first time, some criteria as well as the existence and nonexistence of non-monotone positive solutions are proved in the framework of some properties of solutions $\theta (t)$ of the corresponding integrable linear equation: $(p(t)\theta')'=e(t)$. The main results are illustrated by many examples dealing with equations which allow exact non-monotone positive solutions not necessarily periodic. Finally, we pose some open questions.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA