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Oscillation theorems for Emden-Fowler type delay dynamic equations on time scales. (English) Zbl 1479.34118

Summary: We study the necessary and sufficient conditions for the oscillation of a class of second order half-linear dynamic equations of the form: \[ [a(t)(x^\Delta(t))^\alpha]^\Delta+\psi(t)x^\beta(\delta(t))=0 \] on time scales. The significance of our result is that \(\alpha,\beta\) are quotients of odd positive integers without any restrictive conditions. Some examples are given to illustrate our main results.

MSC:

34K11 Oscillation theory of functional-differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34N05 Dynamic equations on time scales or measure chains
39A10 Additive difference equations
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References:

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