Open Access

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

Advances in Difference Equations20042004:438603

DOI: 10.1155/S1687183904310022

Received: 8 October 2003

Published: 14 December 2004

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.

Authors’ Affiliations

(1)
Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela

Copyright

© Cabada and Vivero 2004