Geodesic
Asymptotic behaviour of oscillatory solutions of $n$-th order differential equations with quasiderivatives
Czechoslovak Mathematical Journal, Tome 47 (1997) no. 2, pp. 245-259 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 34C10, 34C11 
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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/

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