Oscillation criteria for two-dimensional system of non-linear ordinary differential equations
New oscillation criteria are established for the system of non-linear equations $$ u'=g(t)|v|^{\frac{1}{\alpha}}\mathrm{sgn}\,v,\qquad v'=-p(t)|u|^{\alpha}\mathrm{sgn}\,u, $$ where $\alpha>0$, $g:[0,+\infty[{}\rightarrow[0,+\infty[ $, and $p:[0,+\infty[{}\rightarrow \mathbb{R}$ are loc...
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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 |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4929 |
| _version_ | 1797830580754186240 |
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| author | Zdenek Oplustil |
| author_facet | Zdenek Oplustil |
| author_sort | Zdenek Oplustil |
| collection | DOAJ |
| description | New oscillation criteria are established for the system of non-linear equations
$$
u'=g(t)|v|^{\frac{1}{\alpha}}\mathrm{sgn}\,v,\qquad
v'=-p(t)|u|^{\alpha}\mathrm{sgn}\,u,
$$
where $\alpha>0$, $g:[0,+\infty[{}\rightarrow[0,+\infty[ $, and $p:[0,+\infty[{}\rightarrow \mathbb{R}$ are locally integrable functions. Moreover, we assume that the coefficient $g$ is non-integrable on $[0,+\infty]$. Among others, presented oscillatory criteria generalize well-known results of E. Hille and Z. Nehari and complement analogy of Hartman–Wintner theorem for the considered system. |
| first_indexed | 2024-04-09T13:39:25Z |
| format | Article |
| id | doaj.art-63d8d3405fd24bdb8a39f9295250e9ef |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:39:25Z |
| publishDate | 2016-07-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-63d8d3405fd24bdb8a39f9295250e9ef2023-05-09T07:53:05ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752016-07-0120165211710.14232/ejqtde.2016.1.524929Oscillation criteria for two-dimensional system of non-linear ordinary differential equationsZdenek Oplustil0Brno University of Technology, Brno, Czech RepublicNew oscillation criteria are established for the system of non-linear equations $$ u'=g(t)|v|^{\frac{1}{\alpha}}\mathrm{sgn}\,v,\qquad v'=-p(t)|u|^{\alpha}\mathrm{sgn}\,u, $$ where $\alpha>0$, $g:[0,+\infty[{}\rightarrow[0,+\infty[ $, and $p:[0,+\infty[{}\rightarrow \mathbb{R}$ are locally integrable functions. Moreover, we assume that the coefficient $g$ is non-integrable on $[0,+\infty]$. Among others, presented oscillatory criteria generalize well-known results of E. Hille and Z. Nehari and complement analogy of Hartman–Wintner theorem for the considered system.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4929two dimensional system of non-linear differential equationsoscillatory properties |
| spellingShingle | Zdenek Oplustil Oscillation criteria for two-dimensional system of non-linear ordinary differential equations Electronic Journal of Qualitative Theory of Differential Equations two dimensional system of non-linear differential equations oscillatory properties |
| title | Oscillation criteria for two-dimensional system of non-linear ordinary differential equations |
| title_full | Oscillation criteria for two-dimensional system of non-linear ordinary differential equations |
| title_fullStr | Oscillation criteria for two-dimensional system of non-linear ordinary differential equations |
| title_full_unstemmed | Oscillation criteria for two-dimensional system of non-linear ordinary differential equations |
| title_short | Oscillation criteria for two-dimensional system of non-linear ordinary differential equations |
| title_sort | oscillation criteria for two dimensional system of non linear ordinary differential equations |
| topic | two dimensional system of non-linear differential equations oscillatory properties |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4929 |
| work_keys_str_mv | AT zdenekoplustil oscillationcriteriafortwodimensionalsystemofnonlinearordinarydifferentialequations |