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Zbl 1145.34329
Erbe, L.; Peterson, A.; Saker, S.H.
Oscillation and asymptotic behavior of a third-order nonlinear dynamic equation. (English)
[J] Can. Appl. Math. Q. 14, No. 2, 129-147 (2006). ISSN 1073-1849

Summary: We establish some new oscillation criteria for the third-order nonlinear dynamic equation $$(c(t)((a(t)x^\Delta)^\gamma)^\Delta +f(t,x(t))=0,\quad t\in[a,\infty)_{\Bbb T}$$ on time scales, where $\gamma\ge 1$ is a quotient of odd integers. Our results not only unify the oscillation theory for third-order nonlinear differential and difference equations but also are new for the $q$-difference equations and can be applied on different time scales. The results improve some of the main results in the literature in the case when $f = 1$.

MSC 2000:: *34C10 Qualitative theory of oscillations of ODE: Zeros, etc.
39A13 Difference equations, scaling ($q$-differences)
39A10 Difference equations

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Zentralblatt MATH Berlin [Germany]