Non-monotone positive solutions of second-order linear differential equations: existence, nonexistence and criteria (CROSBI ID 232688)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Pašić, Mervan ; Tanaka, Satoshi
engleski
Non-monotone positive solutions of second-order linear differential equations: existence, nonexistence and criteria
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.
non-monotonic behaviour ; positive solutions ; existence ; nonexistence ; criteria
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Podaci o izdanju
2016 (93)
2016.
1-25
objavljeno
1417-3875
10.14232/ejqtde.2016.1.93