Conditionally integrable perturbations of linear differential systems

Abstract

We determine the asymptotic behavior of the solutions of differential systems with conditionally integrable coefficients:

X'= (Δ(t) + V(t))X,  X'= (A + V(t))X.

Where Î”(t)= diag{λ₁(t), Î»₂(t), . . . , Î»_n(t)} satisfies the dichotomic conditions of Levinson's Theorem [5]. A is a constant n x n matrix and V is a conditionally integrable n x n matrix.