Geodesic
On property (B) of higher order delay differential equations
Archivum mathematicum, Tome 48 (2012) no. 4, pp. 301-309 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper we offer criteria for property (B) and additional asymptotic behavior of solutions of the $n$-th order delay differential equations \begin{equation*} \big (r(t)\big [x^{(n-1)}(t)\big ]^{\gamma }\big )^{\prime }=q(t)f\big (x(\tau (t))\big )\,. \end{equation*} Obtained results essentially use new comparison theorems, that permit to reduce the problem of the oscillation of the n-th order equation to the the oscillation of a set of certain the first order equations. So that established comparison principles essentially simplify the examination of studied equations. Both cases $\int ^{\infty } r^{-1/\gamma }(t)\,{t}=\infty $ and $\int ^{\infty } r^{-1/\gamma }(t)\,{t}\infty $ are discussed.
In this paper we offer criteria for property (B) and additional asymptotic behavior of solutions of the $n$-th order delay differential equations \begin{equation*} \big (r(t)\big [x^{(n-1)}(t)\big ]^{\gamma }\big )^{\prime }=q(t)f\big (x(\tau (t))\big )\,. \end{equation*} Obtained results essentially use new comparison theorems, that permit to reduce the problem of the oscillation of the n-th order equation to the the oscillation of a set of certain the first order equations. So that established comparison principles essentially simplify the examination of studied equations. Both cases $\int ^{\infty } r^{-1/\gamma }(t)\,{t}=\infty $ and $\int ^{\infty } r^{-1/\gamma }(t)\,{t}\infty $ are discussed.
DOI : 10.5817/AM2012-4-301
Classification : 34C10, 34K11
Keywords: $n$-th order differential equations; comparison theorem; oscillation; property (B) 
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Baculíková, Blanka; Džurina, Jozef. On property (B) of higher order delay differential equations. Archivum mathematicum, Tome 48 (2012) no. 4, pp. 301-309. doi: 10.5817/AM2012-4-301

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