Nonzero periodic solutions in shifts delta(+/-) for a higher-dimensional nabla dynamic equation on time scales

This paper is concerned with a higher-dimensional neutral nabla dynamic equation on time scales. Based on the theory of calculus on time scales, we first study some properties of the nabla exponential function êA(t,t0) and shift operators δ±, then by using Krasnoselskii's fixed point theorem and contraction mapping principle as well as the obtained results, sufficient conditions are established for the existence of nonzero periodic solutions in shifts S± of the equation as the following form: where A(t) = (aij(t))n×n is a nonsingular matrix with continuous real-valued functions as its elements. Finally, numerical examples are presented to illustrate the applicability of the theoretical results. © 2017, IAENG International Journal of Applied Mathematics. All right reserved.