Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations

Abstract

We prove existence and uniqueness results in the presence of coupled lower and upper solutions for the general n th problem in time scales with linear dependence on the i th 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.