Abstract
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 Δ-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.