Advances in Difference Equations
Volume 2004 (2004), Issue 4, Pages 291-310
doi:10.1155/S1687183904310022
Existence and uniqueness of solutions of higher-order antiperiodic
dynamic equations
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.
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.