A Set of Bounded Solutions of a Linear Weakly Perturbed System

For weakly perturbed systems of linear differential equations, we establish conditions for the point = 0 to bifurcate into a set of solutions bounded on the entire axis R in the case where the corresponding unperturbed homogeneous linear differential system is exponentially dichotomous on the semiaxes R₊ and R_–. We determine the number of linearly independent solutions bounded on R and give an algorithm for finding these solutions.