Positive Periodic Solutions in Shifts δ_± for a Class of Dynamic Equations with Feedback Control on Time Scales

摘要

Let T {is contained in} R be a periodic time scale in shifts δ_± with period P ∈ (t_0, ∞)_T and t_0 ∈ T is 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 shifts δ_± for a class of higher-dimensional functional dynamic equations with feedback control on time scales of the following form: {x~Δ(t) = A(t)x(t) + b(t)f(t,x(τ(t)), u(t)), {u~Δ(t) = -r(t)u(t) + g(t)x(t), t ∈ T, where A(t) = (a_(ij)(t))_(n×n) is 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.