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Zbl 0704.34076
Grace, S.R.
Oscillation of even order nonlinear functional differential equations with deviating arguments.
(English)
[J] Funkc. Ekvacioj, Ser. Int. 32, No.2, 265-272 (1989). ISSN 0532-8721

The functional differential equation $(1)\quad L\sb nx(t)+q(t)f(x[g(t)])=0,$ n is even, is considered. In (1) $L\sb 0x(t)=x(t)$, $L\sb kx(t)=(1/a\sb k(t))(L\sb{k-1}x(t))\sp{\bullet},$ $1\le k\le n$ $(\sp{\bullet}=d/dt)$, $a\sb n=1$, $a\sb i: [t\sb 0,\infty)\to (0,\infty)$, $i=1,2,...,n-1$, q,g: [t${}\sb 0,\infty)\to {\bbfR}$, f: ${\bbfR}\to {\bbfR}$ are continuous, q(t)$\ge 0$ are not identically zero on any ray of the form $[t\sp*,\infty)$ for some $t\sp*\ge t\sb 0$ and $\lim\sb{t\to \infty}g(t)=\infty$. A solution of equation (1) is called oscillatory if it has arbitrary large zeros; otherwise it is called non- oscillatory. Equation (1) is said to be oscillatory if all its solutions are oscillatory. A new oscillation criterion for equation (1) is established.
[B.Cheshankov]
MSC 2000:
*34K99 Functional-differential equations
34A34 Nonlinear ODE and systems, general
34C15 Nonlinear oscillations of solutions of ODE

Keywords: functional differential equation; oscillation criterion

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