Asymptotic behaviour of oscillatory solutions of n -th order differential equations with quasiderivatives

Miroslav Bartušek

Czechoslovak Mathematical Journal (1997)

  • Volume: 47, Issue: 2, page 245-259
  • ISSN: 0011-4642

Abstract

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Sufficient conditions are given under which the sequence of the absolute values of all local extremes of y [ i ] , i ∈ { 0 , 1 , ⋯ , n - 2 } of solutions of a differential equation with quasiderivatives y [ n ] = f ( t , y [ 0 ] , ⋯ , y [ n - 1 ] ) is increasing and tends to ∞ . The existence of proper, oscillatory and unbounded solutions is proved.

How to cite

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Bartušek, Miroslav. "Asymptotic behaviour of oscillatory solutions of $n$-th order differential equations with quasiderivatives." Czechoslovak Mathematical Journal 47.2 (1997): 245-259. <http://eudml.org/doc/30362>.

@article{Bartušek1997,
abstract = {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.},
author = {Bartušek, Miroslav},
journal = {Czechoslovak Mathematical Journal},
keywords = {differential equation with quasiderivatives; proper solution; oscillatory solution; unbounded solution},
language = {eng},
number = {2},
pages = {245-259},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Asymptotic behaviour of oscillatory solutions of $n$-th order differential equations with quasiderivatives},
url = {http://eudml.org/doc/30362},
volume = {47},
year = {1997},
}

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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 47
IS - 2
SP - 245
EP - 259
AB - 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.
LA - eng
KW - differential equation with quasiderivatives; proper solution; oscillatory solution; unbounded solution
UR - http://eudml.org/doc/30362
ER -

References

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