(Q, T)-affine-periodic solutions and Pseudo (Q, T)-affine-periodic solutions for Dynamic Equations on Time Scales

Abstract

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 x Δ t = A t x t + f t and x Δ t = A t x t + g t , x t , 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.