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In this paper, based on the theory of calculus on time scales, by using a multiple fixed point theorem in cones, some criteria are established for the existence and multiplicity of positive periodic solutions in shifts δ± for an impulsive functional dynamic equation 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)), where T⊂R be a periodic time scale in shifts δ± with period P∈[t0,∞)T and t0∈T is nonnegative and fixed. Finally, some numerical examples are presented to illustrate the feasibility and effectiveness of the results.

Multiple periodic solutions in shifts δ ± for an impulsive functional dynamic equation on time scales