On the oscillation of certain second order nonlinear dynamic equations

We establish some new oscillation criteria for solutions to the second order nonlinear dynamic equation (a(x^@D)^@a)^@D(t)+q(t)x^@b(t)=0 on an arbitrary time scale T, where @a and @b are ratios of positive odd integers, a and q are positive rd-continuous functions on T. The results are obtained when @!^~a^-^1^/^@a(s)@Ds<~ or @!^~a^-^1^/^@a(s)@Ds=~. 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.

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