Oscillation criteria for half-linear dynamic equations on time scales (Q930989)

The author considers the second-order half-linear dynamic equation \[ (r(t)(x^{\Delta}(t))^{\gamma})^{\Delta}+p(t)x^{\gamma}(t)=0\tag{1} \] on an arbitrary time scale \(\mathbb{T}\) (\(\sup\mathbb T=\infty\)), where \(\gamma\) is the quotient of odd positive integers, \(r(t)\) and \(p(t)\) are positive rd-continuous functions on \(\mathbb{T}\). Main results of the paper are sufficient conditions for every solution of (1) to be oscillatory. As the author remarks, when \(\mathbb T=\mathbb R\), the obtained results improve several results known for differential equations and when \(\mathbb T=\mathbb N\), then they improve some results known for second order difference equations.