On asymptotic properties of solutions of third order linear differential equations with deviating arguments

Kiguradze, Ivan. "On asymptotic properties of solutions of third order linear differential equations with deviating arguments." Archivum Mathematicum 030.1 (1994): 59-72. <http://eudml.org/doc/247564>.

@article{Kiguradze1994,
abstract = {The asymptotic properties of solutions of the equation $u^\{\prime \prime \prime \}(t)=p_1(t)u(\tau _1(t))+p_2(t)u^\{\prime \}(\tau _2(t))$, are investigated where $p_i:[a,+\infty [\rightarrow R \;\;\;\;(i=1,2)$ are locally summable functions, $\tau _i:[a,+\infty [\rightarrow R\;\;\;(i=1,2)$ measurable ones and $\tau _i(t)\ge t\;\;\;(i=1,2)$. In particular, it is proved that if $p_1(t)\le 0$, $p^2_2(t)\le \alpha (t)|p_1(t)|$, \[\int \_a^\{+\infty \}[\tau \_1(t)-t]^2p\_1(t)dt<+\infty \;\;\;\text\{and\}\;\;\; \int \_a^\{+\infty \}\alpha (t)dt<+\infty ,\] then each solution with the first derivative vanishing at infinity is of the Kneser type and a set of all such solutions forms a one-dimensional linear space.},
author = {Kiguradze, Ivan},
journal = {Archivum Mathematicum},
keywords = {differential equation with deviating arguments; Kneser type solutions; vanishing at infiniting solution; Kneser type solution; third order linear differential equation with deviating arguments},
language = {eng},
number = {1},
pages = {59-72},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On asymptotic properties of solutions of third order linear differential equations with deviating arguments},
url = {http://eudml.org/doc/247564},
volume = {030},
year = {1994},
}

TY - JOUR
AU - Kiguradze, Ivan
TI - On asymptotic properties of solutions of third order linear differential equations with deviating arguments
JO - Archivum Mathematicum
PY - 1994
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 030
IS - 1
SP - 59
EP - 72
AB - The asymptotic properties of solutions of the equation $u^{\prime \prime \prime }(t)=p_1(t)u(\tau _1(t))+p_2(t)u^{\prime }(\tau _2(t))$, are investigated where $p_i:[a,+\infty [\rightarrow R \;\;\;\;(i=1,2)$ are locally summable functions, $\tau _i:[a,+\infty [\rightarrow R\;\;\;(i=1,2)$ measurable ones and $\tau _i(t)\ge t\;\;\;(i=1,2)$. In particular, it is proved that if $p_1(t)\le 0$, $p^2_2(t)\le \alpha (t)|p_1(t)|$, \[\int _a^{+\infty }[\tau _1(t)-t]^2p_1(t)dt<+\infty \;\;\;\text{and}\;\;\; \int _a^{+\infty }\alpha (t)dt<+\infty ,\] then each solution with the first derivative vanishing at infinity is of the Kneser type and a set of all such solutions forms a one-dimensional linear space.
LA - eng
KW - differential equation with deviating arguments; Kneser type solutions; vanishing at infiniting solution; Kneser type solution; third order linear differential equation with deviating arguments
UR - http://eudml.org/doc/247564
ER -