On non-oscillation on semi-axis of solutions of second order deviating differential equations

Sergey Labovskiy; Manuel Alves

Mathematica Bohemica (2018)

  • Volume: 143, Issue: 4, page 355-376
  • ISSN: 0862-7959

Abstract

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We obtain conditions for existence and (almost) non-oscillation of solutions of a second order linear homogeneous functional differential equations u ' ' ( x ) + ∑ i p i ( x ) u ' ( h i ( x ) ) + ∑ i q i ( x ) u ( g i ( x ) ) = 0 without the delay conditions h i ( x ) , g i ( x ) ≤ x , i = 1 , 2 , ... , and u ' ' ( x ) + ∫ 0 ∞ u ' ( s ) d s r 1 ( x , s ) + ∫ 0 ∞ u ( s ) d s r 0 ( x , s ) = 0 .

How to cite

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Labovskiy, Sergey, and Alves, Manuel. "On non-oscillation on semi-axis of solutions of second order deviating differential equations." Mathematica Bohemica 143.4 (2018): 355-376. <http://eudml.org/doc/294617>.

@article{Labovskiy2018,
abstract = {We obtain conditions for existence and (almost) non-oscillation of solutions of a second order linear homogeneous functional differential equations \begin\{equation*\} u^\{\prime \prime \}(x)+\sum \_i p\_i(x) u^\{\prime \}(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 \[ u^\{\prime \prime \}(x)+\int \_0^\{\infty \}u^\{\prime \}(s)\{\rm d\}\_sr\_1(x,s)+\int \_0^\{\infty \} u(s)\{\rm d\}\_sr\_0(x,s) = 0. \]},
author = {Labovskiy, Sergey, Alves, Manuel},
journal = {Mathematica Bohemica},
keywords = {non-oscillation; deviating non-delay equation; singular boundary value problem},
language = {eng},
number = {4},
pages = {355-376},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On non-oscillation on semi-axis of solutions of second order deviating differential equations},
url = {http://eudml.org/doc/294617},
volume = {143},
year = {2018},
}

TY - JOUR
AU - Labovskiy, Sergey
AU - Alves, Manuel
TI - On non-oscillation on semi-axis of solutions of second order deviating differential equations
JO - Mathematica Bohemica
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 143
IS - 4
SP - 355
EP - 376
AB - We obtain conditions for existence and (almost) non-oscillation of solutions of a second order linear homogeneous functional differential equations \begin{equation*} u^{\prime \prime }(x)+\sum _i p_i(x) u^{\prime }(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 \[ u^{\prime \prime }(x)+\int _0^{\infty }u^{\prime }(s){\rm d}_sr_1(x,s)+\int _0^{\infty } u(s){\rm d}_sr_0(x,s) = 0. \]
LA - eng
KW - non-oscillation; deviating non-delay equation; singular boundary value problem
UR - http://eudml.org/doc/294617
ER -

References

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