On non-oscillation on semi-axis of solutions of second order deviating differential equations
We obtain conditions for existence and (almost) non-oscillation of solutions of a second order linear homogeneous functional differential equations \begin{equation*} u"(x)+\sum_i p_i(x) u'(h_i(x))+\sum_i q_i(x) u(g_i(x)) = 0 \end{equation*} without the delay conditions $h_i(x),g_i(x)\l...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Institute of Mathematics of the Czech Academy of Science
2018-12-01
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| Series: | Mathematica Bohemica |
| Subjects: | |
| Online Access: | http://mb.math.cas.cz/full/143/4/mb143_4_3.pdf |
| Summary: | We obtain conditions for existence and (almost) non-oscillation of solutions of a second order linear homogeneous functional differential equations \begin{equation*} u"(x)+\sum_i p_i(x) u'(h_i(x))+\sum_i q_i(x) u(g_i(x)) = 0 \end{equation*} without the delay conditions $h_i(x),g_i(x)\le x$, $i=1,2,\ldots$, and
u"(x)+\int_0^{\infty}u'(s){\rm d}_sr_1(x,s)+\int_0^{\infty} u(s){\rm d}_sr_0(x,s) = 0. |
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| ISSN: | 0862-7959 2464-7136 |