Existence and Uniqueness of Solutions of Higher-order Antiperiodic Dynamic Equations

We prove existence and uniqueness results in the presence of coupled lower and upper solutions for the general nth problem in time scales with linear dependence on the ith ∆derivatives for i= 1,2, . . . ,n, together with antiperiodic boundary value conditions. Here the nonlinear right-hand side of the equation is defined by a function f (t,x) which is rd-continuous in t and continuous in x uniformly in t. To do that, we obtain the expression of the Green’s function of a related linear operator in the space of the antiperiodic functions.