Korol Y. Bounded solutions and integral manifolds of differential equations with degeneracy

This thesis is concerned with investigation of problem of existence boun-ded on the whole axis solution of differential equations with degeneracy, establish sufficient conditions for the existence and asymptotic stability inva-riant sets of degenerate impulsive system of differential equations define on a direct product of m-dimensional torus and n-dimensional Euclidean space. Obtained necessary and sufficient conditions and found bounded on the entire axis solution of degenerate impulsive system, on the assumption that this system reduced to the central canonical form an the nondegenerate homo-geneous system is exponentially dichotomous on the semiaxes. Obtained sufficient conditions of existence and asymptotic stability of integral sets of degenerate linear extension of the non-autonomous system on torus with impulse perturbations at fixed points in time. For ordinary systems and for impulsive system obtained necessary and sufficient conditions for existence of invariant toroidal manifold of a degene-rate linear extension of dynamical system, on the assumption that this system reduced to the central canonical form and the homogeneous nondegenerate system is exponentially dichotomous on the semiaxes.