Boichuk A. Solutions bounded on the whole line R for the systems of ordinary differential equations with perturbations.

3. The thesis is devoted to obtaining conditions for existence of solutions bounded on whole line R of a weakly perturbed linear and nonlinear ordinary differential system under the assumption that the operator defined by the corresponding unperturbed linearized homogeneous system is of Fredholm type. Conditions for the bifurcation from the point ? = 0 of a set of solutions bounded on the whole line R are obtained for a weakly pertubed linear systems of ordinary differential equations under the assumption that the corresponding unpertubed homodeneous linear differential system has an exponential dichotomy on both half-lines R- = (- ?, 0] and R+ = [0, + ?) and the corres-ponding unperturbed linear nonhomogeneous system has no solutions bounded on the whole line R for an arbitrary non-homogeneity. Conditions for existence of solutions bounded on the whole line R for a weakly nonlinear ordinary differential system are obtained under the assumption that the unperturbed linear homogeneous system is of Fredholm type .