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

The authors give sufficient conditions for all solutions of a higher order nonlinear delay dynamic equation on time scales to be nonoscillatory. The results cover both the superlinear and sublinear cases and, in the differential equations case, resolve a question that has been open for 30 years. In order to prove their results, the authors first prove a new Bihari type inequality for functions on time scales.