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Zbl 1205.34134
Lin, Quanwen; Jia, Baoguo; Wang, Qiru
Forced oscillation of second-order half-linear dynamic equations on time scales. (English)
[J] Abstr. Appl. Anal. 2010, Article ID 294194, 10 p. (2010). ISSN 1085-3375; ISSN 1687-0409/e

Summary: We establish a new interval oscillation criterion for the second-order half-linear dynamic equation $$(r(t)[x^\Delta(t)]^\alpha)^\Delta+p(t)x^\alpha(\sigma(t))=f(t)$$ on a time scale $\Bbb T$ which is unbounded. This criterion is an extension of the oscillation result for second order linear dynamic equation established by {\it L. Erbe, A. Peterson} and {\it S. H. Saker} [J. Difference Equ. Appl. 14, No.~10--11, 997--1009 (2008; Zbl 1168.34025)]. As an application, we obtain a sufficient condition for oscillation of the second-order half-linear differential equation $$([x'(t)]^\alpha)'+c\sin tx^\alpha(t)=\cos t,$$ where $\alpha=p/q$, $p, q$ are odd positive integers.

MSC 2000:: *34N05
34C10 Qualitative theory of oscillations of ODE: Zeros, etc.
34K11 Oscillation theory of functional-differential equations

Citations: Zbl 1168.34025

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