Monotonicity conditions in oscillation to superlinear differential equations
We consider the second order differential equation \[ \bigl(a(t)|x^{\prime}|^{\alpha}\operatorname{sgn\,}x^{\prime}\bigr)^{\prime }+b(t)|x|^{\beta}\operatorname{sgn\,}x=0 \] in the super-linear case $\alpha<\beta$. We prove the existence of the so-called intermediate solutions and we discuss thei...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2016-07-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4792 |
| _version_ | 1797830610961563648 |
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| author | Zuzana Dosla Mauro Marini |
| author_facet | Zuzana Dosla Mauro Marini |
| author_sort | Zuzana Dosla |
| collection | DOAJ |
| description | We consider the second order differential equation
\[
\bigl(a(t)|x^{\prime}|^{\alpha}\operatorname{sgn\,}x^{\prime}\bigr)^{\prime
}+b(t)|x|^{\beta}\operatorname{sgn\,}x=0
\]
in the super-linear case $\alpha<\beta$. We prove the existence of the so-called intermediate solutions and we discuss their coexistence with other types of nonoscillatory and oscillatory solutions. Our results are new even for the Emden-Fowler equation ($\alpha=1$). |
| first_indexed | 2024-04-09T13:38:51Z |
| format | Article |
| id | doaj.art-e186f6e31af64f4f8f3deefd3f351ed8 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:38:51Z |
| publishDate | 2016-07-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-e186f6e31af64f4f8f3deefd3f351ed82023-05-09T07:53:05ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752016-07-0120165411310.14232/ejqtde.2016.1.544792Monotonicity conditions in oscillation to superlinear differential equationsZuzana Dosla0Mauro Marini1Masaryk University, Brno, Czech RepublicUniversity of Florence, Firenze, ItalyWe consider the second order differential equation \[ \bigl(a(t)|x^{\prime}|^{\alpha}\operatorname{sgn\,}x^{\prime}\bigr)^{\prime }+b(t)|x|^{\beta}\operatorname{sgn\,}x=0 \] in the super-linear case $\alpha<\beta$. We prove the existence of the so-called intermediate solutions and we discuss their coexistence with other types of nonoscillatory and oscillatory solutions. Our results are new even for the Emden-Fowler equation ($\alpha=1$).http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4792second order nonlinear differential equationnonoscillatory solutionoscillatory solutionintermediate solution |
| spellingShingle | Zuzana Dosla Mauro Marini Monotonicity conditions in oscillation to superlinear differential equations Electronic Journal of Qualitative Theory of Differential Equations second order nonlinear differential equation nonoscillatory solution oscillatory solution intermediate solution |
| title | Monotonicity conditions in oscillation to superlinear differential equations |
| title_full | Monotonicity conditions in oscillation to superlinear differential equations |
| title_fullStr | Monotonicity conditions in oscillation to superlinear differential equations |
| title_full_unstemmed | Monotonicity conditions in oscillation to superlinear differential equations |
| title_short | Monotonicity conditions in oscillation to superlinear differential equations |
| title_sort | monotonicity conditions in oscillation to superlinear differential equations |
| topic | second order nonlinear differential equation nonoscillatory solution oscillatory solution intermediate solution |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4792 |
| work_keys_str_mv | AT zuzanadosla monotonicityconditionsinoscillationtosuperlineardifferentialequations AT mauromarini monotonicityconditionsinoscillationtosuperlineardifferentialequations |