The periodic problem for systems of generalized ordinary differential equations

摘要

In this section, we investigate the solvability for the linear generalized system dx(t) = dA(t) · x(t) + df(t) for t ∈ R (4.1.1) with the ω > 0-periodic condition x(t + ω) = x(t) for t ∈ R, (4.1.2) where ω is a fixed positive number, A= (aik)n i,k=1∈BVω(R; Rn×n) and f = (fi)ni=1∈BVω(R; Rn), i.e., A(t + ω) = A(t) + C and f(t + ω) = f(t) + c for t ∈ R, (4.1.3) where C ∈ Rn×n and c ∈ Rn are, respectively, some constant matrix and constant vector.