Forced Oscillation of Second-Order Half-Linear Dynamic Equations on Time Scales

We will establish a new interval oscillation criterion for second-order half-linear dynamic equation ( r ( t ) [ x Δ ( t ) ] α ) Δ + p ( t ) x α ( σ ( t ) ) = f ( t ) on a time scale T which is unbounded, which is a extension of the oscillation result for second order linear dynamic equation established by Erbe et al. (2008). As an application, we obtain a sufficient condition of oscillation of the second-order half-linear differential equation ( [ x ′ ( t ) ] α ) ′ + c sin t x α ( t ) = cos ⠡ t , where α = p / q , p , q are odd positive integers.