(Q, T)-affine-periodic solutions and Pseudo (Q, T)-affine-periodic solutions for Dynamic Equations on Time Scales - Ruichao Guo; Xiaomeng Jiang; Hongren Wang (Journal of Mathematics)
The aim of this paper is to study the existence of Q,T-affine-periodic solutions for affine-periodic systems on time scales of the type xΔt=Atxt+ft and xΔt=Atxt+gt,xt,t∈T, assuming that corresponding homogeneous equation of this system admits exponential dichotomy. The result is also extended to the case of pseudo Q,T-affine-periodic solutions. The main approaches are based on the Banach contraction mapping principle, but certain technical aspects on time scales are more complicated.