Compactness of cores of targets for nonlinear delay systems

Abstract

The purpose of this study is to investigate the compactness of cores of targets for nonlinear delay systems. Our results are obtained by exploiting the non-singularity of the fundamental matrix for the homogeneous part of the system and its “conjugate” equation. Hajek\'s arguments in [4] of the notion of asymptotic direction and other concepts of convex set theory stand monumental in the development of this study. With a perturbation function, satisfying a smoothness condition – growth condition. A relationship is established between the boundedness of cores of targets and the Euclidean controllability of the nonlinear system. This relationship gives vent to the establishment of the compactness of cores of target for the system. We complement Ukwu [9] and Chukwu [1] by answering in the affirmative that under certain smoothness conditions, the compactness of cores of targets for a linear system guarantees the compactness of cores of target for the linear perturbation. Journal of the Nigerian Association of Mathematical Physics Vol. 8 2004: pp. 101-104