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

Czechoslovak Mathematical Journal (1997)

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

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topBartušek, 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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