## Forced oscillation of second-order half-linear dynamic equations on time scales.(English)Zbl 1205.34134

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 $$\mathbb T$$ which is unbounded. This criterion is an extension of the oscillation result for second order linear dynamic equation established by L. Erbe, A. Peterson and 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:

 34N05 Dynamic equations on time scales or measure chains 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34K11 Oscillation theory of functional-differential equations

Zbl 1168.34025
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### References:

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