Advances in Difference Equations
Volume 2004 (2004), Issue 4, Pages 291-310

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

Alberto Cabada and Dolores R. Vivero

Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, Galicia, Santiago de Compostela 15782, Spain

Received 8 October 2003; Revised 9 February 2004

Copyright © 2004 Alberto Cabada and Dolores R. Vivero. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.