Positive Periodic Solutions in Shifts δ± for a Class of Higher-Dimensional Functional Dynamic Equations with Impulses on Time Scales - Meng Hu; Lili Wang; Zhigang Wang (Abstract and Applied Analysis)
Let T⊂R be a periodic time scale in shifts δ± with period P∈(t0,∞)T and t0∈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 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)), 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 feasibility and effectiveness of the results.