We obtain comparison theorems for the second-order half-linear dynamic equation , where with . In particular, it is shown that the nonoscillation of the previous dynamic equation is preserved if we multiply the coefficient by a suitable function and lower the exponent in the nonlinearity , under certain assumptions. Moreover, we give a generalization of Hille-Wintner comparison theorem. In addition to the aspect of unification and extension, our theorems provide some new results even in the continuous and the discrete case.
"On certain comparison theorems for half-linear dynamic equations on time scales." Abstr. Appl. Anal. 2004 (7) 551 - 565, 29 June 2004. https://doi.org/10.1155/S1085337504306251