Oscillation and nonoscillation of perturbed higher order Euler-type differential equations
Oscillatory properties of even order self-adjoint linear differential equations in the form $$ \sum_{k=0}^{n} (-1)^k\nu_k\left(\frac{y^{(k)}}{t^{2n-2k-\alpha}}\right)^{(k)} =(-1)^m\left(q_m(t)y^{(m)}\right)^{(m)},\; \nu_n:=1, $$ where $m \in \{0, 1\}$, $\alpha \not\in \{1, 3, \dots , 2n-1\}$ and $...
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2005-06-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=221 |
| Summary: | Oscillatory properties of even order self-adjoint linear differential equations in the form
$$
\sum_{k=0}^{n}
(-1)^k\nu_k\left(\frac{y^{(k)}}{t^{2n-2k-\alpha}}\right)^{(k)}
=(-1)^m\left(q_m(t)y^{(m)}\right)^{(m)},\; \nu_n:=1,
$$
where $m \in \{0, 1\}$, $\alpha \not\in \{1, 3, \dots , 2n-1\}$ and $\nu_0, \dots, \nu_{n-1},$ are real constants satisfying certain conditions, are investigated. In particular, the case when $q_m(t)=\frac{\beta}{t^{2n-2m-\alpha}\ln^2 t }$ is studied. |
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| ISSN: | 1417-3875 1417-3875 |