Oscillatory Behavior of Nonlinear Second-Order Dynamic Equations on Time Scales

The study of dynamic equations on time scales is a fairly new subject. and research in this area is rapidly growing. It allows a simultaneous treatment of differential and difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a time scale. In this way results not only related to the set of real numbers or the set of integers but those pertaining to more general time scales are obtained. In this paper. some sufficient conditions are established for the oscillation of certain nonlinear second-order dynamic equations on time scales by making use of a generalized Riccati transformation technique. The results in this paper improve and extend some known results in the literature.