Monotone solutions of dynamic systems on time scales

and rðtÞ :1⁄4 sup{t , t : t [ T}; for all t [ T, where inf Y: 1⁄4 sup T and sup Y: 1⁄4 inf T, where Y denotes the empty set. We assume throughout that T has the topology that it inherits from the standard topology on the real numbers R. If s(t) . t, we say t is right-scattered, while if r(t) , t we say t is leftscattered. If s(t) 1⁄4 t and t , sup T we say t is right-dense, while if r(t) 1⁄4 t and t . inf T we say t is left-dense. The function x:T ! R is said to be right-dense continuous (rd-continuous) and we write x [ Crd provided x is continuous at each right-dense point in T and at each left-dense point in T left-hand limits exist (finite). The function x:T ! R is said to be regressive provided the regressivity condition