On the oscillation of certain second order nonlinear dynamic equations

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Abstract

We establish some new oscillation criteria for solutions to the second order nonlinear dynamic equation (a(xΔ)α)Δ(t)+q(t)xβ(t)=0 on an arbitrary time scale T, where α and β are ratios of positive odd integers, a and q are positive rd-continuous functions on T. The results are obtained when a1/α(s)Δs< or a1/α(s)Δs=. These criteria unify and extend known results for the corresponding half-linear and nonlinear differential and difference equations. Some of our results are new even in the continuous and discrete cases.

Keywords

Oscillation
Nonoscillation
Dynamic equation
Half-linear

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