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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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 |
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doaj-56a5c03978504a12800ce742d1bab67d2021-07-14T07:21:19ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38751417-38752005-06-0120051312110.14232/ejqtde.2005.1.13221Oscillation and nonoscillation of perturbed higher order Euler-type differential equationsSimona Fišnarová0Mendel University in Brno, Brno, Czech RepublicOscillatory 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.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=221 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Simona Fišnarová |
| spellingShingle |
Simona Fišnarová Oscillation and nonoscillation of perturbed higher order Euler-type differential equations Electronic Journal of Qualitative Theory of Differential Equations |
| author_facet |
Simona Fišnarová |
| author_sort |
Simona Fišnarová |
| title |
Oscillation and nonoscillation of perturbed higher order Euler-type differential equations |
| title_short |
Oscillation and nonoscillation of perturbed higher order Euler-type differential equations |
| title_full |
Oscillation and nonoscillation of perturbed higher order Euler-type differential equations |
| title_fullStr |
Oscillation and nonoscillation of perturbed higher order Euler-type differential equations |
| title_full_unstemmed |
Oscillation and nonoscillation of perturbed higher order Euler-type differential equations |
| title_sort |
oscillation and nonoscillation of perturbed higher order euler-type differential equations |
| publisher |
University of Szeged |
| series |
Electronic Journal of Qualitative Theory of Differential Equations |
| issn |
1417-3875 1417-3875 |
| publishDate |
2005-06-01 |
| description |
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. |
| url |
http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=221 |
| work_keys_str_mv |
AT simonafisnarova oscillationandnonoscillationofperturbedhigherordereulertypedifferentialequations |
| _version_ |
1721303821649444864 |