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Zbl 1202.34162
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan; Saker, Samir H.
Interval oscillation criteria for forced second-order nonlinear delay dynamic equations with oscillatory potential. (English)
[J] Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 17, No. 4, 533-542 (2010). ISSN 1201-3390; ISSN 1918-2538/e

From the text: We are concerned with the oscillation of a second-order nonlinear delay dynamic equation of the form $$(r(t)x^\Delta(t))^\Delta+q(t)f(x(\tau(t)))=g(t),\tag*$$ on a time scale $\Bbb T$, where $r(t)$, $q(t)$, and $g(t)$ are $rd$-continuous functions with $r(t)\le \sigma(t)$ and $\lim f_{\infty}\tau(t)=\infty$. The function $f\in C(\Bbb R,\Bbb R)$ is assumed to satisfy $uf(u) > 0$, for $u\ne 0$ and $|f(u)|\ge k|u|$, for some $k>0$. Our interest in this paper is to establish some oscillation criteria for (*) that do not assume that $q(t)$ and $g(t)$ are of definite sign.

MSC 2000:: *34N05
34K11 Oscillation theory of functional-differential equations

Keywords: oscillation; forced delay dynamic equations; time scales

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