Philos-type oscillation criteria for second order half-linear dynamic equations on time scales. (English) Zbl 1139.34029

Agarwal, Ravi P.; O’Regan, Donal; Saker, S. H.

Rocky Mt. J. Math. 37, No. 4, 1085-1104 (2007).

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:

34C10	Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
39A10	Additive difference equations

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