Positive periodic solutions in shifts Delta(+/-) for a neutral dynamic equation on time scales

摘要

ublishercopyright>? 2018 International Association of Engineers.? 2018 International Association of Engineers. In this paper, based on the theory of calculus on time scales, by using Krasnoselskii's fixed point theorem and contraction mapping principle, sufficient conditions are established for the existence of positive periodic solutions in shifts δ± for a neutral functional dynamic equation on time scales of the following form: x Δ = -a(t)x(t) + f Δ (t, x(t)) + b(t)g(t, x(τ(t))), t∈ T, where T ? ? be a periodic time scale in shifts δ± with period P ∈ [t 0 ,∞)T and t 0 ∈ T is nonnegative and fixed. Finally, some numerical examples are presented to illustrate the feasibility and effectiveness of the results. In this paper, based on the theory of calculus on time scales, by using Krasnoselskii's fixed point theorem and contraction mapping principle, sufficient conditions are established for the existence of positive periodic solutions in shifts δ± for a neutral functional dynamic equation on time scales of the following form: x ΔΔ = -a(t)x(t) + f ΔΔ (t, x(t)) + b(t)g(t, x(τ(t))), t∈ T, where T ? ? be a periodic time scale in shifts δ± with period P ∈ [t 00 ,∞)T and t 00 ∈ T is nonnegative and fixed. Finally, some numerical examples are presented to illustrate the feasibility and effectiveness of the results.