Nonoscillation of all solutions of a higher order nonlinear delay dynamic equation on time scales (Q472374)

This interesting paper discusses an \(n\)-th order nonlinear forced dynamic equation with delay on a times scale. By deriving a Bihari type inequality on time scales, the authors obtain sufficient conditions for all solutions to be nonoscillatory. The main approach is to use the forcing term to stop oscillation. We point out that the problem of finding conditions for all solutions to be nonoscillatory is much harder than that of finding conditions for all solutions to be oscillatory, and even harder that of finding conditions for some solutions to be nonoscillatory. Restricted to differential equations, this work resolves a question that has been open for 30 years.