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Philos-type oscillation criteria for second order half-linear dynamic equations on time scales. (English) Zbl 1139.34029
Summary: We establish some oscillation theorems for the second order half-linear dynamic equation $$(r(t)(x^\Delta(t))^\gamma)^\Delta+ p(t)x^\gamma(t) = 0,\quad t\in [a, b],$$ on time scales. Special cases of our results include some well-known oscillation results for second-order differential and half-linear differential equations. Our results are new for difference, generalized difference and $q$ difference half-linear equations.

MSC:
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
39A10Additive difference equations
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Full Text: DOI Euclid
References:
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