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Zbl 1082.34032
Saker, S.H.
Oscillation criteria of second-order half-linear dynamic equations on time scales. (English)
[J] J. Comput. Appl. Math. 177, No. 2, 375-387 (2005). ISSN 0377-0427

The subject of the paper is oscillation of solutions of second-order delta differential equations of the type $$(p(t)(x^\Delta(t))^\gamma)^\Delta+q(t)x^\gamma(t)=0\tag 1$$ on quite general time scales. Here, $\gamma>1$ is an odd positive integer and $p,\ q$ are positive right-dense continuous functions. The function $(1/p)^{1/ \gamma}$ may be integrable (in the sense of time scale analysis) at $+\infty$ or not. Sufficient conditions for the oscillatory character of all non-trivial solutions of (1) are given in both cases. The main theorems are applicable, in particular, to half-linear difference equations and half-linear ordinary differential equations, unifying and extending previous results. At the end of the paper, some examples are discussed to illustrate the range of applicability of the main results.
[Luis Sanchez (Lisboa)]

MSC 2000:: *34C10 Qualitative theory of oscillations of ODE: Zeros, etc.
39A12 Discrete version of topics in analysis

Keywords: oscillation; second-order half-linear dynamic equations; time scale

Cited in: Zbl 1180.34069

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