Positive Periodic Solutions in Shiftsδ±for a Class of Higher-Dimensional Functional Dynamic Equations with Impulses on Time Scales

Abstract

LetT⊂Rbe a periodic time scale in shiftsδ±with periodP∈(t0,∞)Tandt0∈Tis nonnegative and fixed. By using a multiple fixed point theorem in cones, some criteria are established for the existence and multiplicity of positive solutions in shiftsδ±for a class of higher-dimensional functional dynamic equations with impulses on time scales of the following form:xΔ(t)=A(t)x(t)+b(t)f(t,x(g(t))),  t≠tj,  t∈T,  x(tj+)=x(tj-)+Ij(x(tj)),whereA(t)=(aij(t))n×nis a nonsingular matrix with continuous real-valued functions as its elements. Finally, numerical examples are presented to illustrate the feasibility and effectiveness of the results.