Asymptotic behaviour of oscillatory solutions of $n$-th order differential equations with quasiderivatives
Czechoslovak Mathematical Journal, Tome 47 (1997) no. 2, pp. 245-259
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Sufficient conditions are given under which the sequence of the absolute values of all local extremes of $y^{[i]}$, $i\in \lbrace 0,1,\dots , n-2\rbrace $ of solutions of a differential equation with quasiderivatives $y^{[n]}=f(t,y^{[0]},\dots , y^{[n-1]})$ is increasing and tends to $\infty $. The existence of proper, oscillatory and unbounded solutions is proved.
@article{CMJ_1997__47_2_a4,
author = {Bartu\v{s}ek, Miroslav},
title = {Asymptotic behaviour of oscillatory solutions of $n$-th order differential equations with quasiderivatives},
journal = {Czechoslovak Mathematical Journal},
pages = {245--259},
publisher = {mathdoc},
volume = {47},
number = {2},
year = {1997},
mrnumber = {1452419},
zbl = {0930.34023},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMJ_1997__47_2_a4/}
}
TY - JOUR AU - Bartušek, Miroslav TI - Asymptotic behaviour of oscillatory solutions of $n$-th order differential equations with quasiderivatives JO - Czechoslovak Mathematical Journal PY - 1997 SP - 245 EP - 259 VL - 47 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/CMJ_1997__47_2_a4/ LA - en ID - CMJ_1997__47_2_a4 ER -
%0 Journal Article %A Bartušek, Miroslav %T Asymptotic behaviour of oscillatory solutions of $n$-th order differential equations with quasiderivatives %J Czechoslovak Mathematical Journal %D 1997 %P 245-259 %V 47 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/CMJ_1997__47_2_a4/ %G en %F CMJ_1997__47_2_a4
Bartušek, Miroslav. Asymptotic behaviour of oscillatory solutions of $n$-th order differential equations with quasiderivatives. Czechoslovak Mathematical Journal, Tome 47 (1997) no. 2, pp. 245-259. http://geodesic.mathdoc.fr/item/CMJ_1997__47_2_a4/