Asymptotic behavior of solutions of asymptotically constant coefficient systems of linear differential equations

Sufficient conditions are given for the n × n system yʹ=(A+P(t))y to have a solution such that as t → ∞, where λ is an eigenvalue of the constant matrix A and v is an associated eigenvector. The integrability conditions on P allow conditional convergence and the o(1) terms are specified precisely.