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 |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4929 |
| Summary: | 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. |
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| ISSN: | 1417-3875 1417-3875 |