Hartman-type comparison theorems for half-linear differential equations of the second order
Comparison theorem of the Hartman type for a continuous family of nonlinear differential equations of the form $$ \big(p(t, \lambda)\varphi(u')\big)' + q(t,\lambda) \varphi(u) = 0, \lambda \geq 0, \quad \tag{ $\rm E_\lambda$}$$ where $ p \in \mathrm{C}([a,b]\times [0,\infty), (0,\infty)),...
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| Format: | Article |
| Language: | English |
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University of Szeged
2012-10-01
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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=1804 |
| Summary: | Comparison theorem of the Hartman type for a continuous family of nonlinear differential equations of the form
$$ \big(p(t, \lambda)\varphi(u')\big)' + q(t,\lambda) \varphi(u) = 0, \lambda \geq 0, \quad \tag{ $\rm E_\lambda$}$$
where $ p \in \mathrm{C}([a,b]\times [0,\infty), (0,\infty)), q \in \mathrm{C}([a,b] \times [0,\infty),\mathbb{R}), i = 1, ..., n,$ and $\varphi(s) :=|s|^{\alpha-1} s$ for $s \not= 0$ and $\varphi (0) = 0$, is proved with the help of the generalized Mingarelli's identity. |
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| ISSN: | 1417-3875 |